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56 papers · 1 filter
Garsia--Remmel -rook numbers are not always unimodal
Joel Brewster Lewis, Alejandro H. Morales
We show by an explicit example that the Garsia--Remmel -rook numbers of Ferrers boards do not all have unimodal sequences of coefficients. This resolves in the negative a questi…
Coincidences between intervals in two partial orders on complex reflection groups
Joel Brewster Lewis, Jiayuan Wang
In a finite real reflection group, the reflection length of each element is equal to the codimension of its fixed space, and the two coincident functions determine a partial order…
Hurwitz numbers for reflection groups III: Uniform formulas
Theo Douvropoulos, Joel Brewster Lewis, Alejandro H. Morales
We give uniform formulas for the number of full reflection factorizations of a parabolic quasi-Coxeter element in a Weyl group or complex reflection group, generalizing the formula…
Connectivity gaps among matroids with the same enumerative invariants
Joseph E. Bonin, Kevin Long
Many important enumerative invariants of a matroid can be obtained from its Tutte polynomial, and many more are determined by two stronger invariants, the -invariant a…
A characterization of positroids, with applications to amalgams and excluded minors
Joseph E. Bonin
A matroid of rank on elements is a positroid if it has a representation by an by matrix over , each by submatrix of which has nonnegative determ…
Enumeration of Payphone Permutations
Max A. Alekseyev
The desire for privacy significantly impacts various aspects of social behavior as illustrated by people's tendency to seek out the most secluded spot when multiple options are ava…