Combinatorics/Algebra Seminar: Spring 2001 Archive

April 23
Maria Axenovich: Report from the 32nd Southeastern Conference
April 16
Alex Burstein: Packing density of layered patterns II
April 2
Maria Axenovich: Domination in edge-colored graphs
March 26
Alex Burstein: Packing density of layered patterns
March 5
Joy Becker: Invariance of unary operations
February 26
Alex Burstein: Layered patterns
February 5
Ji Young Choi: Multi-restricted numbers and powers of permutation representations

Abstract: Let G be a transitive permutation group on a set Q. The orbit
decompositions of the actions of G on the sets of ordered n-tuples
from Q with elements repeated at most m times are studied. The
decompositions involve Stirling numbers and a new class of related
numbers, the so-called multi-restricted numbers. The talk presents
exponential generating functions for the numbers of orbits, and examines
relationships between various powers of the G-set involving Stirling
numbers and the multi-restricted numbers. Moreover, a three-term
recurrence formula for the multi-restricted numbers is obtained.

January 29
Anna Romanowska: Varieties of binary modes II
January 22
Anna Romanowska: Varieties of binary modes I
January 8
Charles Johnson, College of William and Mary:
Determinantal inequalities: ancient history and recent advances
(Special Colloquium: will be held in 408 Carver)

Abstract: We begin by describing classical determinantal inequalities involving
principal minors of positive definite matrices due to Hadamard, Fischer, and
Koteljanskii. In the mid to later 1900's there was much work giving particular
generalizations of these inequalities for positive definite matrices,
M-matrices, inverse M-matrices and totally positive matrices. We finish by
describing a modern effort to characterize all bounded ratios of products of
principal minors within a class of matrices, a major thrust of modern matrix

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