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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
Totally nonnegative maximal tori and opposed Bruhat intervals
Grant T. Barkley, Steven N. Karp
Lusztig (2024) recently introduced the space of totally positive maximal tori of an algebraic group . Each such torus is the intersection of a totally positiv…
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…