3 citations · 5 across the 8 of their papers we have counts for
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A counterexample to a log-concavity conjecture of Brenti
Christian Gaetz
This note records a counterexample to Brenti's 1998 conjecture that the nonzero coefficients of -polynomials form a log-concave sequence.
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…
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…
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…
The commutant of divided difference operators, Klyachko's genus, and the comaj statistic
Christian Gaetz, Rebecca Goldin, Allen Knutson
In [Hamaker-Pechenik-Speyer-Weigandt, Nenashev, Pechenik-Weigandt] are studied certain operators on polynomials and power series that commute with all divided difference operators…
A note on Combinatorial Invariance of Kazhdan--Lusztig polynomials
Francesco Esposito, Mario Marietti, Grant T. Barkley +1
We introduce the concepts of an amazing hypercube decomposition and a double shortcut for it, and use these new ideas to formulate a conjecture implying the Combinatorial Invarianc…
On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials
Grant T. Barkley, Christian Gaetz
We show that the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials due to Lusztig and to Dyer, its parabolic analog due to Marietti, and a refined parabolic versi…
Combinatorial invariance for Kazhdan-Lusztig -polynomials of elementary intervals
Grant T. Barkley, Christian Gaetz
We adapt the hypercube decompositions introduced by Blundell-Buesing-Davies-Veličković-Williamson to prove the Combinatorial Invariance Conjecture for Kazhdan-Lusztig -polynomia…