CanaDAM 2011
Université de Victoria, 31 mai - 3 juin 2011


ALEJANDRO ERICKSON, University of Victoria
Enumerating Tatami Tilings  [PDF]

A monomer-dimer tiling in which no four tiles touch at any point has the {\em tatami} property. Tatami tilings are visually pleasing and have a known structure. This structure and some of its implications will be described, followed by a mostly visual presentation, showing that the number of tatami tilings of the $n\times n$ grid is equal to $2^{n-1}(3n-4)+2$ (which is also the sum of the squares of all parts in all compositions of $n$).

ELIZABETH MCMAHON, Lafayette College
Derangements of the facets of the $n$-cube  [PDF]

The number of automorphisms of an $n$-cube is $2^n n!$. How many of those are derangements on the facets of the cube? The answer is a sequence that has been studied in several other contexts. We give combinatorial proofs of the equivalence of several formulas for that sequence. Whether a derangement is odd or even depends on whether the underlying isometry is direct or indirect. We also discuss generalizations.

ALOIS PANHOLZER, Vienna University of Technology
Some new results for deriving hook-length formulas for trees  [PDF]

Starting with a remarkable hook-length formula for binary trees obtained by Postnikov various works in the combinatorial literature are devoted to proving and establishing such kind of identities. Here we present several new results in this research direction. In particular we propose an expansion technique for weighted tree families, which unifies and extends recent results obtained by Han and Chen et al. Furthermore we give combinatorial and probabilistic proofs of several new/recent hook-length formulas.

JOSE PLINIO SANTOS, UNICAMP-Universidade Estadual de Campinas
Bijections between lattice paths and plane partitions  [PDF]

In a previous paper we gave a new combinatorial interpretation for partitions as two-line matrices. Our main goal in the present one is to associate a three-line matrix to a lattice path in 3-dimensional space, in order to build a volume, which is going to correspond to a plane partition. In this way it is possible to construct bijections between certain classes of plane partitions and overpartitions. A similar result for unrestricted partitions is given.

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Centre de recherches mathématiques Fields Institute MITACS Pacific Institute for the Mathematical Sciences Société mathématique du Canada University of Victoria