2 citations · 2 across the 5 of their papers we have counts for
7 papers · 1 filter
Non-attacking rook placements on crossword grids
Joel Brewster Lewis, Robert Won
We introduce the notion of a non-attacking rook placement on a crossword grid. A crossword grid is a collection of white squares (which comprise across and down words) and black sq…
Counting factorizations of Singer cycles in linear and unitary groups
Joel Brewster Lewis, C. Ryan Vinroot
We count factorizations of Singer cycles as products of reflections in the families of special and general unitary and linear groups over a finite field. In the case of minimum-len…
Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks
Sergi Elizalde, Nadia Lafrenière, Joel Brewster Lewis +3
We find a generating function for interval-closed sets of the product of two chains poset by constructing a bijection to certain bicolored Motzkin paths. We also find a functional…
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…