Colin Defant

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math.CO2026

Short Proofs in Algebraic and Enumerative Combinatorics

Colin Defant

We present several short proofs that resolve open problems from the algebraic and enumerative combinatorics literature. First, we consider the echelonmotion operator on modular lat…

math.CO2026

Weak Order on the MacNeille Completion of Bruhat Order

Colin Defant

Let $Mac (W)$ be the MacNeille completion of the Bruhat order of a Coxeter group $W$ . We introduce an action of the $0$ -Hecke monoid of type $W$ on $Mac (W)$ , which…

math.CO2024

0-Hecke Modules, Domino Tableaux, and Type- $B$ Quasisymmetric Functions

Colin Defant, Dominic Searles

We extend the notion of ascent-compatibility from symmetric groups to all Coxeter groups, thereby providing a type-independent framework for constructing families of modules of $0$ …

Short Proofs in Algebraic and Enumerative Combinatorics

Weak Order on the MacNeille Completion of Bruhat Order

0-Hecke Modules, Domino Tableaux, and Type-B Quasisymmetric Functions

0-Hecke Modules, Domino Tableaux, and Type- $B$ Quasisymmetric Functions