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Contributed Minisymposia
There will be contributed minisymposia in the following areas.
Applications of Generating Functions
Organizer and Chair: Alois Panholzer (Technische Universität Wien)
Starting with Leonard Euler's computation of the number of triangulations of a convex $n$-gon generating functions are an indispensable tool in combinatorial enumeration. Generating functions allow to apply algebraic and analytic techniques and thus might be considered as a bridge between both ``worlds''. Often inspired by concrete problems from the analysis of algorithms and data structures, powerful analytic combinatorics methods have been developed to describe the asymptotic behaviour of quantities in random structures. In this minisymposium several such recent results will be presented, where generating functions techniques play an essential r\^{o}le.
Marie-Louise Bruner (Vienna University of Technology, Austria), Bernhard Gittenberger (Technische Universität Wien), Helmut Prodinger (Stellenbosch University), Alfredo Viola (Universidad de la República), Mark Daniel Ward (Purdue University).
Applied Combinatorics and the Natural Sciences I
Chair: Chris Soteros (University of Saskatchewan)
Org: Marni Mishna (Simon Fraser University), Chris Soteros (University of Saskatchewan) and Karen Yeats (Simon Fraser University)
The natural sciences provide a rich source of inspiration for discrete mathematics. The proposed minisymposia (2 sessions with 4-5 speakers each) bring together researchers with a common interest in combinatorial modelling of natural phenomena in chemistry, physics and biology. Areas of application include: phase transitions, models of DNA/RNA, and quantum field theory. Combinatorial approaches include: integral and functional equation methods, kernel method, Monte Carlo and random generation schemes. The session speakers reflect a mixture of applied combinatorics expertise: some focussed more on the analytical and computational tools while others focussed more on the applications. This cross-fertilization at the interface between discrete mathematics and the natural sciences will inspire improvements both in the models and in the combinatorial analysis.
Iain Crump (Simon Fraser University, Canada), Marni Mishna (Simon Fraser University, Canada), Aleks Owczarek (University of Melbourne, Australia), Michael Szafron (University of Saskatchewan, Canada), Stuart Whittington (University of Toronto, Canada).
Applied Combinatorics and the Natural Sciences II
Chair: Marni Mishna (Simon Fraser University)
Org: Marni Mishna (Simon Fraser University), Chris Soteros (University of Saskatchewan) and Karen Yeats (Simon Fraser University)
The natural sciences provide a rich source of inspiration for discrete mathematics. The proposed minisymposia (2 sessions with 4-5 speakers each) bring together researchers with a common interest in combinatorial modelling of natural phenomena in chemistry, physics and biology. Areas of application include: phase transitions, models of DNA/RNA, and quantum field theory. Combinatorial approaches include: integral and functional equation methods, kernel method, Monte Carlo and random generation schemes. The session speakers reflect a mixture of applied combinatorics expertise: some focussed more on the analytical and computational tools while others focussed more on the applications. This cross-fertilization at the interface between discrete mathematics and the natural sciences will inspire improvements both in the models and in the combinatorial analysis.
Tom Boothby (Simon Fraser University), Sophie Burrill (Simon Fraser University, Canada), E. J. Janse van Rensburg (York University, Canada), Chris Soteros (University of Saskatchewan, Canada), Karen Yeats (Simon Fraser University, Canada).
Chromatic Graph Theory
Organizer and Chair: Joan P. Hutchinson (Macalester College, emerita)
Coloring graphs has interested practicioners since the beginning of graph theory. Over time a wide variety of approaches has been developed, turning the field into one of continuing interest and connection with other branches of graph theory and its applications. In this mini-symposium we sample a range of topics: edge-coloring and its connections with Hamiltonicity; list-coloring and its uses with graphs on surfaces, planar and nonplanar; and algorithms and complexity of injective and frugal colorings and related homomorphisms.
Joan Hutchinson (Macalester College), Gary MacGillivray (University of Victoria), Luke Postle (Emory University), Stan Wagon (Macalester College).
Cycle Decompositions of Graphs I
Chair: Mateja Sajna (University of Ottawa)
Org: Andrea Burgess (Ryerson University) and Mateja Sajna (University of Ottawa)
In the last 15 years, enormous progress has been made in the area of cycle decompositions of graphs. A breakthrough was made by Alspach, Jordon and \v{S}ajna, who determined necessary and sufficient conditions for the existence of an $m$-cycle decomposition of the complete graph $K_n$. In 2011, this result was extended to complete multigraphs by Bryant, Horsley, Maenhaut, and Smith. Perhaps even more impressive are the 2012 complete solution to the long-outstanding Alspach's conjecture on decomposing complete graphs into cycles of various lengths by Bryant, Horsley, and Pettersson, and the first solution to the Oberwolfach Problem for an infinite set of orders by Bryant and Scharaschkin. Many other results on cycle decompositions of various graphs and with various prescribed properties have been proved during this time. In this 2-part minisymposium, we would like to gather some of the researchers who have contributed most to this flourishing research area.
Darryn Bryant (University of Queensland), Andrea Burgess (Ryerson University), Peter Danziger (Ryerson University), Daniel Horsley (Monash University), Barbara Maenhaut (University of Queensland).
Cycle Decompositions of Graphs II
Chair: Andrea Burgess (Ryerson University)
Org: Andrea Burgess (Ryerson University) and Mateja Sajna (University of Ottawa)
In the last 15 years, enormous progress has been made in the area of cycle decompositions of graphs. A breakthrough was made by Alspach, Jordon and \v{S}ajna, who determined necessary and sufficient conditions for the existence of an $m$-cycle decomposition of the complete graph $K_n$. In 2011, this result was extended to complete multigraphs by Bryant, Horsley, Maenhaut, and Smith. Perhaps even more impressive are the 2012 complete solution to the long-outstanding Alspach's conjecture on decomposing complete graphs into cycles of various lengths by Bryant, Horsley, and Pettersson, and the first solution to the Oberwolfach Problem for an infinite set of orders by Bryant and Scharaschkin. Many other results on cycle decompositions of various graphs and with various prescribed properties have been proved during this time. In this 2-part minisymposium, we would like to gather some of the researchers who have contributed most to this flourishing research area.
Marco Buratti (Università degli Studi di Perugia), Danny Dyer (Memorial University), Heather Jordon (American Mathematical Society), Sibel Ozkan (Gebze Institute of Technology), Mateja Sajna (University of Ottawa).
Decidability in Automatic and Related Sequences
Organizer and Chair: Jeffrey Shallit (University of Waterloo)
A sequence $(a(n))$ over a finite alphabet is said to be $k$-automatic if there is a deterministic finite automaton that, on input $n$ expressed in base $k \geq 2$, reaches a state with output $a(n)$; a typical example is the classical Thue-Morse sequence. The recent realization that many questions about these sequences can be phrased in the logical theory $(\mathbb{N}, +, <, V_k)$, where $V_k(n)$ is the highest power of $k$ dividing $n$, leads to a decision procedure for answering these questions. In this mini-symposium we will describe this decision procedure and look at some of its many ramifications. Using the decision procedure, we can reprove many results in the literature and find new ones. Although the worst-case running time of the decision procedure is very bad, an implementation often succeeds in mechanically proving the assertions in question. We also address the limitations of the method.
James Currie (University of Winnipeg), Daniel Goc (University of Waterloo), Narad Rampersad (University of Winnipeg), Luke Schaeffer (University of Waterloo), Jeffrey Shallit (University of Waterloo).
Discrete Math Coast to Coast: Newfoundland and the West
Chair: Kseniya Garaschuk (University of Victoria)
Org: Gary MacGillivray (University of Victoria)
This two-part minisymposium features a speaker from each province, where "from" means was born there, or educated there, or grew up there. One of the goals is for the talks to reflect the richness and diversity of discrete mathematics across Canada. The speakers in this part are "from" Newfoundland, BC, Alberta, Saskatchewan, and Manitoba.
Kathleen Barnetson (Memorial University of Newfoundland), Kseniya Garaschuk (University of Victoria), Shonda Gosselin (University of Winnipeg), Karen Meagher (University of Regina), Bill Sands (University of Calgary).
Discrete Math Coast to Coast: The Maritimes and the Middle
Chair: Chris Duffy (University of Victoria)
Org: Gary MacGillivray (University of Victoria)
This two-part minisymposium features a speaker from each province, where "from" means was born there, or educated there, or grew up there. One of the goals is for the talks to reflect the richness and diversity of discrete mathematics across Canada. The speakers in this part are "from" New Brunswich, Nova Scotia, PEI, Quebec and Ontario.
Nancy Clarke (Acadia University), Chris Duffy (University of Victoria), Shannon Fitzpatrick (University of Prince Edward Island), Margaret-Ellen Messinger (Mount Allison University), Ben Seamone (Universite de Montreal).
Domination in Graphs
Organizer and Chair: Gary MacGillivray (University of Victoria)
Domination is one of the most studied topics in graph theory. The goal of this minisymposuim is to string together five talks on recent progress in different aspects of this broad area.
Rick Brewster (Thompson Rivers University), Michelle Edwards (University of Victoria), Stephen Finbow (St. Francis Xavier), Ruth Haas (Smith College), Ortrud Oellermann (University of Winnipeg).
Eric Mendelsohn: Colleagues and Descendants I
Chair: Brett Stevens (Carleton University)
Org: Peter Danziger (Ryerson University) and Brett Stevens (Carleton University)
These minisymposia celebrate the influence and work of Eric Mendelsohn through his collaborators, students, and other colleagues. At age 1, Eric Mendelsohn was a registered participant at the inaugural 1945 Montreal meeting of the Canadian Mathematics Society. His activities and influence in discrete mathematics continue to this day. He was hired at the Department of Mathematics at the University of Toronto in 1970, where he has been full professor since 1982. He retired from the University in 2010, and is now professor emeritus. He is currently an adjunct professor with the department of Mathematics at Ryerson University, whose support we gratefully acknowledge. Eric has 94 publications, 55 co-authors, 13 official "descendants". He has been an important force in combinatorics and discrete mathematics over many years, his energy and vision have provided many important directions and insights.
Jason Brown (Dalhousie University), Nevena Francetic (Carleton University), Karen Meagher (University of Regina), Douglas Stinson (University of Waterloo).
Eric Mendelsohn: Colleagues and Descendants II
Chair: Brett Stevens (Carleton University)
Org: Peter Danziger (Ryerson University) and Brett Stevens (Carleton University)
These minisymposia celebrate the influence and work of Eric Mendelsohn through his collaborators, students, and other colleagues. At age 1, Eric Mendelsohn was a registered participant at the inaugural 1945 Montreal meeting of the Canadian Mathematics Society. His activities and influence in discrete mathematics continue to this day. He was hired at the Department of Mathematics at the University of Toronto in 1970, where he has been full professor since 1982. He retired from the University in 2010, and is now professor emeritus. He is currently an adjunct professor with the department of Mathematics at Ryerson University, whose support we gratefully acknowledge. Eric has 94 publications, 55 co-authors, 13 official "descendants". He has been an important force in combinatorics and discrete mathematics over many years, his energy and vision have provided many important directions and insights.
Robert Bailey (Ryerson University), Derek Corneil (University of Toronto), Peter Dukes (University of Victoria), Nabil Shalaby (Memorial University of Newfoundland).
Eric Mendelsohn: Colleagues and Descendants III
Chair: Peter Danziger (Ryerson University)
Org: Peter Danziger (Ryerson University) and Brett Stevens (Carleton University)
These minisymposia celebrate the influence and work of Eric Mendelsohn through his collaborators, students, and other colleagues. At age 1, Eric Mendelsohn was a registered participant at the inaugural 1945 Montreal meeting of the Canadian Mathematics Society. His activities and influence in discrete mathematics continue to this day. He was hired at the Department of Mathematics at the University of Toronto in 1970, where he has been full professor since 1982. He retired from the University in 2010, and is now professor emeritus. He is currently an adjunct professor with the department of Mathematics at Ryerson University, whose support we gratefully acknowledge. Eric has 94 publications, 55 co-authors, 13 official "descendants". He has been an important force in combinatorics and discrete mathematics over many years, his energy and vision have provided many important directions and insights.
Aiden Bruen (Carleton University), Frantisek Franek (McMaster University), Sebastian Raaphorst (University of Ottawa), Ben Seamone (University de Montreal), Daniela Silvesan (Memorial University of Newfoundland).
Finite Fields in Combinatorics I
Chair: David Thomson (Carleton University)
Org: Petr Lisonek (Simon Fraser University) and David Thomson (Carleton University)
The areas of finite fields and combinatorics are strongly linked. The talks in this minisymposium highlight the versatility in the use of finite fields to construct interesting classes of combinatorial objects and prove results about them. Topics addressed in the talks include error control codes, finite geometries, planar functions, Costas and related arrays, sequences with good correlation properties, permutation polynomials, decomposition of polynomials, and more.
Aiden Bruen (Carleton University), Kenza Guenda (University of Victoria), Petr Lisonek (Simon Fraser University), Jane Wodlinger (University of Victoria), Yue Zhou (Otto-von-Guericke University of Magdeburg).
Finite Fields in Combinatorics II
Chair: Petr Lisonek (Simon Fraser University)
Org: Petr Lisonek (Simon Fraser University) and David Thomson (Carleton University)
The areas of finite fields and combinatorics are strongly linked. The talks in this minisymposium highlight the versatility in the use of finite fields to construct interesting classes of combinatorial objects and prove results about them. Topics addressed in the talks include error control codes, finite geometries, planar functions, Costas and related arrays, sequences with good correlation properties, permutation polynomials, decomposition of polynomials, and more.
Mark Giesbrecht (University of Waterloo), Jing He (Carleton University), Xiang-dong Hou (University of South Florida), Daniel Katz (California State University, Northridge), David Thomson (Carleton University).
Galois Geometries and Applications I
Chair: Jan De Beule (Ghent University)
Org: Jan De Beule (Ghent University) and Petr Lisonek (Simon Fraser University)
Galois geometries is the research field in which projective spaces over the finite fields, also called Galois fields, are investigated. This includes the study of their substructures and their links to other research areas. Many of these substructures are investigated for their geometrical importance, such as the quadrics and the Hermitian varieties, but many substructures are investigated because of their links to other research areas such as coding theory. This includes the link between arcs in Galois geometries and linear MDS codes. Recently, also links between random network coding and Galois geometries have been found. The techniques used in Galois geometries involve, next to geometrical techniques, also other techniques such as the polynomial method. This minisymposium will discuss different aspects of Galois geometries. This includes theoretical results and links to coding theory.
Kathryn Haymaker (University of Nebraska - Lincoln, USA), Petr Lisonek (Simon Fraser University, Canada), Brett Stevens (Carleton University, Canada), Peter Sziklai (Eotvos Lorand University, Budapest, Hungary), Qing Xiang (University of Delaware, USA).
Galois Geometries and Applications II
Chair: Petr Lisonek (Simon Fraser University)
Org: Jan De Beule (Ghent University) and Petr Lisonek (Simon Fraser University)
Galois geometries is the research field in which projective spaces over the finite fields, also called Galois fields, are investigated. This includes the study of their substructures and their links to other research areas. Many of these substructures are investigated for their geometrical importance, such as the quadrics and the Hermitian varieties, but many substructures are investigated because of their links to other research areas such as coding theory. This includes the link between arcs in Galois geometries and linear MDS codes. Recently, also links between random network coding and Galois geometries have been found. The techniques used in Galois geometries involve, next to geometrical techniques, also other techniques such as the polynomial method. This minisymposium will discuss different aspects of Galois geometries. This includes theoretical results and links to coding theory.
Michael Braun (University of Darmstadt, Germany), Jan De Beule (Ghent University, Belgium), Maarten De Boeck (Ghent University, Belgium), Sara Rottey (VUB (Vrije Universiteit Brussel), Belgium), Alfred Wassermann (University of Bayreuth, Germany).
Geometric Representations of Graphs
Organizer and Chair: Steven Chaplick (Charles University, Prague, Czech Republic)
Visualizations and representations of graphs by means of intersections or contacts of geometric objects have been widely investigated. Classical examples are interval graphs and Koebe circle representations. When representations are given they can sometimes be exploited in optimization problems. In many instances these problems are hard for general graphs but become polynomial-time solvable when restricted to intersection or contact graphs with a given representations. Another class of problems is to compute the representation or to decide whether it exists. In this minisymposium we highlight some recent developments in this active area at the intersection of graph theory and discrete geometry.
Steven Chaplick (Charles University, Prague, Czech Republic), Anna Lubiw (University of Waterloo, Waterloo, Canada), Marcus Schaefer (DePaul University, Chicago, U.S.A.), Torsten Ueckerdt (Karlsruhe Institute of Technology, Karlsruhe, Germany), Ryuhei Uehara (Japan Advanced Institute of Science and Technology, Nomi, Japan).
Graph Homomorphisms
Organizer and Chair: Pavol Hell (SFU)
The speakers will focus on recent results concerning various aspects of graph homomorphisms
Patrice Ossona de Mendez (L'Ecole des Hautes Etudes en Sciences Sociales, Paris), Laszlo Egri (Hungarian Academy of Sciences, Budapest), Hamed Hatami (McGill University, Montreal), Jaroslav Nesetril (Charles University, Prague), Robert Samal (Charles University, Prague).
Graph Structure and Algorithms
Organizer and Chair: Kathie Cameron (Wilfrid Laurier University)
Often graphs arising in applications have special structure. This structure can sometimes be used to design efficient algorithms for problems that are hard in general. Clearly, special structure is needed to prove the existence of certain types of subgraphs which do not exist in more general graphs. In this minisymposium, we see four instances of efficient algorithms and existence theorems which exploit special structure, and one anomalous algorithmic problem which was solved by ignoring the special graph structure.
Kathie Cameron (Wilfrid Laurier University), Jessica Enright (University of Glasgow), Elaine Eschen (West Virginia University), R. Sritharan (University of Dayton), Katie Tsuji (University of Waterloo).
Graph Theory with Applications in Chemistry I
Chair: Patrick Fowler (University of Sheffield)
Org: Patrick Fowler (University of Sheffield) and Wendy Myrvold (University of Victoria)
This session and the following linked session explore applications of graph theory to chemistry. Part I includes contributions on graph theory with applications to currents in molecules. Ballistic currents driven through molecules in an electric circuit and ring current circulations generated within aromatic molecules by a magnetic field are both of importance in chemistry and materials science, and both can be modelled using techniques from spectral graph theory and the theory of perfect matchings. Speakers will discuss some of these models and the connections between them.
Matthias Ernzerhof (University of Montreal), Patrick W Fowler (University of Sheffield), Wendy Myrvold (University of Victoria), Barry T Pickup (University of Sheffield), Irene Sciriha (University of Malta).
Graph Theory with Applications in Chemistry II
Chair: Wendy Myrvold (University of Victoria)
Org: Patrick Fowler (University of Sheffield) and Wendy Myrvold (University of Victoria)
This session and the previous linked session explore applications of graph theory to chemistry. Part II includes contributions on graph theory with applications to molecular structure, stability and reactivity. Stability and properties of fullerenes and benzenoids are of theoretical and practical interest in chemistry, and are often modelled using theories based on perfect matchings and graph spectra. Talks will include discussion of two models of fullerene (and benzenoid) stability based on the ideas proposed by Clar and Fries, extension of graph spectral models to saturated systems, and new models of chemical reactivity.
Jack E Graver (Syracuse University), Elizabeth Hartung (Massachusetts College of Liberal Arts), Douglas J Klein (Texas A&M University at Galveston), Craig E Larson (Virginia Commonwealth University), Nico Van Cleemput (University of Gent).
Gray Codes and Universal Cycles
Chair: Joe Sawada (University of Guelph)
Org: Joe Sawada (University of Guelph) and Aaron Williams (McGill University)
The ability to efficiently generate all possible instances of a particular combinatorial object (permutations, combinations, trees, necklaces, etc) is of practical importance to many areas of scientific research. It is the primary topic in Knuth's most recent addition to his series ``The Art Of Computer Programming''. This session will focus on several key aspects in this area including: (Greedy) Gray codes, Universal cycles, Random generation. In particular, attendees may learn simple ways to construct their ``family tree'' and how to ``greedily flip pancakes''.
Joe Sawada (University of Guelph), Xi Sisi Shen (McGill University), Ryuhei Uehara (Japan Advanced Institute of Science and Technology), Aaron Williams (McGill University).
Hypergraphs
Chair: Amin Bahmanian (University of Ottawa)
Org: Amin Bahmanian and Mateja Sajna (University of Ottawa)
In the last decade, hypergraph theory has emerged as a powerful mathematical tool in a variety of real-life applications. However, in spite of its remarkable developments, the theory of hypergraphs has not yet given rise to extensive literature comparing to the theory of graphs. For example, very little is known about edge decompositions of hypergraphs, even for special cases. Perhaps the best evidence for the difficulty of questions about hypergraphs is Sylvester's Problem, which asks about the existence of a 1-factorization of the complete uniform hypergraph. It took 120 years before Baranyai finally solved this problem. The goal of this minisymposium is to bring together experts in various areas of hypergraph theory. The main areas of interest are edge colorings, edge decompositions, amalgamations, detachments, and embeddings.
Amin Bahmanian (University of Ottawa), Andrzej Czygrinow (Arizona State University), Shonda Gosselin (University of Winnipeg), Imdadullah Khan (Umm Al Qura University), Mateja Sajna (University of Ottawa).
Independence Number: Theory and Applications I.
Chair: Craig Larson (Virginia Commonwealth University)
Org: Ermelinda DeLaVina (University of Houston--Downtown) and Craig Larson (Virginia Commonwealth University)
Researchers will present recent work related to the independence structure of a graph. Several speakers discuss advances in the investigation of well-covered graphs, graphs where every maximal independent set is a maximum independent set. Other research includes new bounds for the independence number, new bounds for the number of independent structures, and theory and problems related to the efficient computation of the independence number.
Ermelinda DeLaVina (University of Houston--Downtown), Art Finbow (Saint Mary's University), Michael D. Plummer (Vanderbilt University), William Staton (University of Mississippi), David Tankus (Ariel University of Samaria).
Independence Number: Theory and Applications II.
Chair: Ermelinda DeLaVina (University of Houston--Downtown)
Org: Ermelinda DeLaVina (University of Houston--Downtown) and Craig Larson (Virginia Commonwealth University)
Researchers will present recent work related to the independence structure of a graph. Several speakers discuss advances in the investigation of well-covered graphs, graphs where every maximal independent set is a maximum independent set. Other research includes new bounds for the independence number, new bounds for the number of independent structures, and theory and problems related to the efficient computation of the independence number.
Jochen Harant (Ilmenau University of Technology), Bert Hartnell (Saint Mary's University), Craig Larson (Virginia Commonwealth University), Ryan Pepper (University of Houston--Downtown), Doug Rall (Furman University).
Nested Recurrence Relations
Organizer and Chair: Frank Ruskey (University of Victoria)
Hofstadter introduced the recurrence $Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2))$, an example of a \textit{nested recurrence relation} (or NRR) because it has a sub-expression of the form $…Q(…Q(…)…)…$. Other than composition, the only operations that are used are addition/subtraction. Recently there has been a flurry of activity in trying to understand and ``solve'' NRRs. Some NRRs have a solution and combinatorial interpretations, while others seemingly do not. It is still unknown whether $Q(n)$ is defined for all $n$. On the other hand, the recurrence $T(n)=T(n-1-T(n-1))+T(n-2-T(n-2))$ with $T(1)=T(2)=T(3)=1$, the number $T(n)$ counts the maximum number of leaves at the lowest level in a $n$-node binary tree. There are many recent results that show that NRRs arise from natural counting problems in certain classes of highly structured infinite trees. There are undecidable NRRs and some that are related to automatic sequences. This minisymposium will introduce NRRs, present some recent results, and offer tantalizing open problems.
Marcel Celaya (McGill University), Mustazee Rahman (University of Toronto), Frank Ruskey (University of Victoria), Jeff Shallit (University of Waterloo), Steve Tanny (University of Toronto).
Partitioning Graphs into Independent Sets and Cliques
Organizer and Chair: Dennis D.A. Epple (University of Victoria)
A natural generalization of graph colourings is to consider partitions of the vertex set of graphs into independent sets and cliques. This idea gives rise to a wide field of topics including $(k,l)$-colourings, split graphs, the cochromatic number, and matrix partitions. This minisymposium features a broad selection of current research in the area.
Tınaz Ekim (Boğaziçi University), Dennis D.A. Epple (University of Victoria), Pavol Hell (Simon Fraser University), Mayssam Mohammadi Nevisi (Simon Fraser University), Juraj Stacho (University of Warwick).
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