Combinatorics Seminar - Spring 2014
Room 226, Goldsmith building
The Combinatorics Seminar is an introductory seminar for combinatorics. The talk should be accesible to first year graduate students.
Monday March 10
Speaker: Yiting Li
Title: Menage numbers and Menage permutation
Abstract: A straight Menage permutation is a permutation $\pi\in S_n$ such that $\pi(i)$ is neither $i$ nor $i+1$. An ordinary Menage
permutation is a permutation $\pi\in S_n$ such that $\pi(i)$ is
neither $i$ nor $i+1 \mod n$. The numbers of straight (ordinary)
Menage permutations in $S_n$ are called straight (ordinary)
Menage numbers. In this talk I'll prove two formulas for the
generating functions of straight and ordinary Menage numbers. I'll
also give the formulas which count straight and ordinary Menage
permutations by cycles.
Monday March 17
Speaker: Olivier Bernardi
Title: Counting the spanning trees of the hypercube
Abstract: I will present two combinatorial proofs of a counting
formula for the spanning trees of the hypercube. One of the proof highlights mysterious independence property for the directions of edges in the
uniformly random spanning tree of the hypercube.