29 citations · 203 across the 38 of their papers we have counts for
39 papers
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…
Princ-wiki-a Mathematica: Wikipedia editing and mathematics
David Eppstein, Joel Brewster Lewis, Russ Woodroofe +1
Over the past 20 years, Wikipedia has gone from a rather outlandish idea to a major reference work, with more than 60 million articles across all languages, including nearly 7 mill…
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…
-analogues of some properties of -cycles in
Joel Brewster Lewis
We give analogues in the finite general linear group of two elementary results concerning long cycles and transpositions in the symmetric group: first, that the long cycles are pre…
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…
Bargain hunting in a Coxeter group
Joel Brewster Lewis, Bridget Eileen Tenner
Petersen and Tenner defined the depth statistic for Coxeter group elements which, in the symmetric group, can be described in terms of a cost function on transpositions. We general…
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…
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…
A Random Card Shuffling Process
Joel Brewster Lewis, Mehr Rai
Consider a randomly shuffled deck of cards with red cards and black cards. We study the average number of moves it takes to go from a randomly shuffled deck to a deck…
Hurwitz numbers for reflection groups I: Generatingfunctionology
Theo Douvropoulos, Joel Brewster Lewis, Alejandro H. Morales
The classical Hurwitz numbers count the fixed-length transitive transposition factorizations of a permutation, with a remarkable product formula for the case of minimum length (gen…
The Hurwitz action in complex reflection groups
Joel Brewster Lewis, Jiayuan Wang
We enumerate Hurwitz orbits of shortest reflection factorizations of an arbitrary element in the infinite family of complex reflection groups. As a consequence, we cha…
The path-missing and path-free complexes of a directed graph
Darij Grinberg, Lukas Katthän, Joel Brewster Lewis
We study two simplicial complexes arising from a directed graph with two chosen vertices and : the *path-free complex*, consisting of all subsets $F \subseteq E…
The tree search game for two players
Ravi B. Boppana, Joel Brewster Lewis
We consider a two-player search game on a tree . One vertex (unknown to the players) is randomly selected as the target. The players alternately guess vertices. If a guess i…
A note on the Hurwitz action on reflection factorizations of Coxeter elements in complex reflection groups
Joel Brewster Lewis
We show that the Hurwitz action is "as transitive as possible" on reflection factorizations of Coxeter elements in the well-generated complex reflection groups (the gr…
Scaling limit of soliton lengths in a multicolor box-ball system
Joel Lewis, Hanbaek Lyu, Pavlo Pylyavskyy +1
The box-ball systems are integrable cellular automata whose long-time behavior is characterized by soliton solutions, with rich connections to other integrable systems such as the…
Enriched set-valued P-partitions and shifted stable Grothendieck polynomials
Joel Brewster Lewis, Eric Marberg
We introduce an enriched analogue of Lam and Pylyavskyy's theory of set-valued -partitions. An an application, we construct a -theoretic version of Stembridge's Hopf algebra…
Factorization problems in complex reflection groups
Joel Brewster Lewis, Alejandro H. Morales
We enumerate factorizations of a Coxeter element in a well generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In…
An affine generalization of evacuation
M. Chmutov, G. Frieden, D. Kim +2
We establish the existence of an involution on tabloids that is analogous to Schutzenberger's evacuation map on standard Young tableaux. We find that the number of its fixed points…
Reflection length in the general linear and affine groups
Elise G. delMas, Joel Brewster Lewis
We give an intrinsic criterion to tell whether a reflection factorization in the general linear group is reduced, and give a formula for computing reflection length in the general…
Rook theory of the finite general linear group
Joel Brewster Lewis, Alejandro H. Morales
Matrices over a finite field having fixed rank and restricted support are a natural -analogue of rook placements on a board. We develop this -rook theory by defining a corres…
Monodromy in Kazhdan-Lusztig cells in affine type A
Michael Chmutov, Joel Brewster Lewis, Pavlo Pylyavskyy
We use the affine Robinson-Schensted correspondence to describe the structure of bidirected edges in the Kazhdan-Lusztig cells in affine type A. Equivalently, we give a comprehensi…