8 papers
When Lexical Change Misleads: Rethinking Dynamic Topic Model Evaluation with Traditional and LLM-Based Metrics
Charu Karakkaparambil James
Dynamic topic models capture evolving word distributions, but traditional coherence metrics may fail when vocabulary changes while semantic meaning persists. We evaluate 120 topics…
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, VeliÄkoviÄ, and Williamson (BBDVW) introduced the notion of a hypercube decomposition of an interval in Bruhat order. They conjectured a recursive form…
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-VeliÄkoviÄ-Williamson to prove the Combinatorial Invariance Conjecture for Kazhdan-Lusztig -polynom…