17 citations · 78 across the 24 of their papers we have counts for
32 papers
Noncrossing Combinatorics, the Full Twist, and Decategorification of Knot Invariants
Colin Defant, Nathan Williams
Much work in knot theory has consisted of categorifying, and thereby strengthening, knot invariants. We take the opposite approach: decategorification, more commonly called combina…
Wiener Indices of Minuscule Lattices
Colin Defant, Valentin Féray, Philippe Nadeau +1
The Wiener index of a finite graph G is the sum over all pairs (p, q) of vertices of G of the distance between p and q. When P is a finite poset, we define its Wiener index as the…
The Ungar Games
Colin Defant, Noah Kravitz, Nathan Williams
Let be a finite lattice. An Ungar move sends an element to the meet of , where is a subset of the set of elements covered by . We introduce the fol…
Charmed roots and the Kroweras complement
Benjamin Dequêne, Gabriel Frieden, Alessandro Iraci +3
Although both noncrossing partitions and nonnesting partitions are uniformly enumerated for Weyl groups, the exact relationship between these two sets of combinatorial objects rema…
Pop, Crackle, Snap (and Pow): Some Facets of Shards
Colin Defant, Nathan Williams
Reading cut the hyperplanes in a real central arrangement into pieces called \emph{shards}, which reflect order-theoretic properties of the arrangement. We show that s…
Rational Noncrossing Coxeter-Catalan Combinatorics
Pavel Galashin, Thomas Lam, Minh-Tâm Quang Trinh +1
We solve two open problems in Coxeter-Catalan combinatorics. First, we introduce a family of rational noncrossing objects for any finite Coxeter group, using the combinatorics of d…