MS-2 Combinatorial Matrix Theory

Organizers: Minerva Catral (Xavier University, OH) and Louis Deaett (Quinnipiac University)

Connections between linear algebra and combinatorics have yielded rich interactions between the two areas and have led to a great deal of interesting and important mathematics. A matrix can be viewed through a combinatorial lens in a variety of ways, for example via a description such as a matrix pattern that retains only discrete information from the matrix, e.g., the signs of the entries, or by using a graph or directed graph to describe various constraints on the matrix. One may then ask what information such a combinatorial description can carry about the operator-theoretic properties of the matrix, such as its rank or its spectrum. Moreover, classes of matrices with discrete entries, such as Hadamard and alternating sign matrices, form an important area of study in combinatorics, and one in which the role of linear algebra is naturally central. This mini-symposium will feature recent advances and questions of current interest in these areas.

Speakers

Mohsen Aliabadi, On matching in groups and vector spaces

Ravindra Bapat, Squared distance matrix of a weighted tree

Jane Breen, Minimising the largest mean first passage time of a Markov chain and the influence of directed graphs

Richard A Brualdi, The Permutation and Alternating Sign Matrix Rational Cones

Louis Deaett, Matroids and the minimum rank problem for zero-nonzero patterns

Wei Gao, Tree Sign Patterns that Require ℍn

Colin Garnett, Combinatorial and Algebraic Conditions that preclude SAPpiness

Mª José Jiménez, Triangular matrices and combinatorial recurrences

Franklin Kenter, Computational Approaches for Minimum Rank Problems and their Variations

Stephen Kirkland, (0,1) Matrices and the Analysis of Social Networks

Zhongshan Li, Sign patterns that allow diagonalizability

Xavier Martinez-Rivera, The signed epr-sequence

Judi McDonald, Spectrally Arbitrary Patterns over Different Fields

Shahla Nasserasr, Distinct eigenvalues of graphs

Polona Oblak, The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph

Bryan Shader, A Matrix Rank Identity with Applications to Combinatorial Matrices

Kevin Vander Meulen, Recursive constructions for spectrally arbitrary patterns

Xiaohong Zhang, Hadamard diagonalizable graphs used to transfer quantum information