3 papers
math.CO2026
Bounded Bruhat intervals and affine Coxeter groups
Grant T. Barkley, Christian Gaetz
Dyer (1991) proved that, for each fixed length , only finitely many isomorphism types of Bruhat intervals occur in finite Coxeter groups. In this short paper, we prove that this…
math.CO2026
Combinatorial invariance for the coefficient of in Kazhdan-Lusztig polynomials
Grant T. Barkley, Christian Gaetz, Thomas Lam
We prove the combinatorial invariance of the coefficient of in Kazhdan--Lusztig polynomials for arbitrary Coxeter groups. As a result, we obtain the Combinatorial Invariance Co…
math.CO2024
The BBDVW Conjecture for Kazhdan-Lusztig polynomials of lower intervals
Grant T. Barkley, Christian Gaetz
Blundell, Buesing, Davies, Veličković, and Williamson (BBDVW) introduced the notion of a hypercube decomposition of an interval in Bruhat order. They conjectured a recursive formul…