5 papers
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…
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…
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…