Browsing Mathematics by Author "Billey, Sara C"
Now showing items 1-5 of 5
-
Combinatorics and Representation Theory of Rank Varieties, Springer Fibers, and Hyperplane Arrangements
Griffin, SeanThis thesis is dedicated to applications of symmetric function theory to problems in combinatorics, representation theory, and geometry. Crucial to our applications is the Frobenius characteristic map from Algebraic ... -
Flavors of the Fubini-Bruhat Order
Ryan, StarkFubini words are generalized permutations, allowing for repeated letters, and theyare in one-to-one correspondence with ordered set partitions. Brendan Pawlowski and Brendon Rhoades extended permutation matrices to pattern ... -
Major Index Statistics: Cyclic Sieving, Branching Rules, and Asymptotics
Swanson, JoshuaMajor index statistics have been studied for over a century in many guises and appear throughout algebraic combinatorics. We pursue major index statistics from two complementary perspectives: algebraic and asymptotic. We ... -
Pattern Avoidance Criteria for Smoothness of Positroid Varieties Via Decorated Permutations, Spirographs, and Johnson Graphs
Weaver, Jordan E.Positroids are certain representable matroids originally studied by Postnikov in connection with the totally nonnegative Grassmannian and now used widely in algebraic combinatorics. The positroids give rise to determinantal ... -
Permutation diagrams in symmetric function theory and Schubert calculus
Pawlowski, BrendanA fundamental invariant of a permutation is its inversion set, or diagram. Natural machinery in the representation theory of symmetric groups produces a symmetric function from any finite subset of <bold>N</bold><super>2</super>, ...