17 citations · 78 across the 24 of their papers we have counts for
7 papers · 1 filter
Sweeping up Zeta
Hugh Thomas, Nathan Williams
Using techniques introduced by H. Thomas and N. Williams in "Cyclic Symmetry of the Scaled Simplex," we prove that modular sweep maps are bijective. We construct the inverse of the…
Automata, reduced words, and Garside shadows in Coxeter groups
Christophe Hohlweg, Philippe Nadeau, Nathan Williams
In this article, we introduce and investigate a class of finite deterministic automata that all recognize the language of reduced words of a finitely generated Coxeter system (W,S)…
Strange Expectations
Marko Thiel, Nathan Williams
Let gcd(a,b)=1. J. Olsson and D. Stanton proved that the maximum number of boxes in a simultaneous (a,b)-core is (a^2-1)(b^2-1)/24, and that this maximum was achieved by a unique c…
Braid moves in commutation classes of the symmetric group
Anne Schilling, Nicolas M. Thiéry, Graham White +1
We prove that the expected number of braid moves in the commutation class of the reduced word for the long…
Noncrossing partitions and Bruhat order
Thomas Gobet, Nathan Williams
We prove that the restriction of Bruhat order to noncrossing partitions in type for the Coxeter element forms a distributive lattice isomorphic to the order…
Cataland: Why the Fuss?
Christian Stump, Hugh Thomas, Nathan Williams
The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of thes…