Seminar

Title: Bijections among symmetric tableaux via folding and mixed insertion

Abstract:

A standard Young tableau with entries $-M < \cdots -1 < 1 < \cdots < M$ can be "folded" by performing certain conversions and rectifications in sequence.

Title: Stable marraige with general preferences

Abstract:

This week, we discuss a generalization of the standard stable marriage problem, in which one side has a complete, totally ordered, strict preference list while the other has preferences given in terms of arbitrary binary relations.

Title: Kemeny's Constant for Markov Chains

Abstract:

Markov chains are a much-studied class of stochastic processes, and it is well-known that if the transition matrix A associated with a Markov chain possesses a certain property (called primitivity), then the long-term behaviour of the Markov chain is described by a particular eigenvector of A, known as the stationary distribution vector.

Title: New and Simple Algorithms for Stable Flow Problems

Abstract:

In the previous reading group talk we defined stable flows and saw that they always exist by a reduction to the stable allocation problem.

Title: Graphs in algebra and algebra in graphs

Abstract:

How do algebraic properties of a graph relate to its graph theoretic properties? What are algebraic properties of graphs? What does the spectrum of a graph tell us about its structure? What is a Cayley graph?

Title: Lewis Carroll and the Red Hot Potato

Abstract:

The Lewis Carroll identity expresses the determinant of a matrix in terms of subdeterminants obtained by deleting one row and column or a pair of rows and columns.

Title: Reverse plane partitions via quiver representations

Abstract:

Let $\lambda$ be a partition. The reverse plane partitions of shape $\lambda$ are a kind of filling of the Ferrers diagram of $\lambda$ by non-negative integers. Richard Stanley found the generating function which enumerates them according to the sum of the entries.

Title: Stable Flows

Abstract:

We describe a flow model that generalizes ordinary network flows the same way as stable matchings generalize the bipartite matching problem.

Title: Incidence bialgebras of monoidal categories

Abstract:

We begin with Joni and Rota's definition of the incidence coalgebra of a category or partially ordered set and then discuss some cases where a monoidal product on a category turns this coalgebra into a bialgebra.

Title: From Combinatorics to Computer Algebra and Morse Theory - Making Sense of Multivariate Asymptotics

Abstract:

The  asymptotic study  of  multivariate  generating  functions comprises  the  domain  of  Analytic Combinatorics  in Several Variables (ACSV).