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5 papers · 2 filters
Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements
Theo Douvropoulos, Joel Brewster Lewis, Alejandro H. Morales
We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associ…
The excluded minors for three classes of 2-polymatroids having special types of natural matroids
Joseph E. Bonin, Kevin Long
If is a minor-closed class of matroids, the class of integer polymatroids whose natural matroids are in is also minor closed, as is the c…
The natural matroid of an integer polymatroid
Joseph E. Bonin, Carolyn Chun, Tara Fife
The natural matroid of an integer polymatroid was introduced to show that a simple construction of integer polymatroids from matroids yields all integer polymatroids. As we illustr…
Combinatorial formulas for shifted dual stable Grothendieck polynomials
Joel Brewster Lewis, Eric Marberg
The -theoretic Schur - and -functions and may be concretely defined as weight generating functions for semistandard shifted set-valued tableaux. These symmet…
In which it is proven that, for each parabolic quasi-Coxeter element in a finite real reflection group, the orbits of the Hurwitz action on its reflection factorizations are distinguished by the two obvious invariants
Theo Douvropoulos, Joel Brewster Lewis
We prove that two reflection factorizations of a parabolic quasi-Coxeter element in a finite Coxeter group belong to the same Hurwitz orbit if and only if they generate the same su…