Flip Combinatorial Invariance and Weyl groups

2025/09/19 by Francesco Esposito, Esposito, Francesco, Mario Marietti +3
Engineering · Mathematics · #graph theory and CDMA systems #Advanced Combinatorial Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2509.16433

Abstract

In this work, we investigate the approach via flipclasses to the Combinatorial Invariance Conjecture for Kazhdan--Lusztig polynomials of all Coxeter groups. We prove the combinatorial invariance of Kazhdan--Lusztig \widetildeR-polynomials of Weyl groups modulo q⁷ and of Kazhdan--Lusztig \widetildeR-polynomials of type A Weyl groups modulo q⁸. As a consequence, the Combinatorial Invariance Conjecture holds for all intervals up to length 8 in Weyl groups and up to length 10 in type A Weyl groups.

Citations

• A note on Combinatorial Invariance of Kazhdan--Lusztig polynomials
• Flipclasses and Combinatorial Invariance for Kazhdan--Lusztig polynomials
• Parabolic recursions for Kazhdan-Lusztig polynomials and the hypercube decomposition
• Weak generalized lifting property, Bruhat intervals and Coxeter matroids
• The combinatorial invariance conjecture for parabolic Kazhdan-Lusztig\n polynomials of lower intervals
• Imaginary cones and limit roots of infinite Coxeter groups
• Reflection subgroups of finite and affine Weyl groups
• Sortable elements and Cambrian lattices
• Clusters, Coxeter-sortable elements and noncrossing partitions

Related

• Flipclasses and Combinatorial Invariance for Kazhdan--Lusztig polynomials
• The combinatorial invariance conjecture for parabolic Kazhdan-Lusztig\n polynomials of lower intervals
• A note on Combinatorial Invariance of Kazhdan--Lusztig polynomials
• Invariance Combinatoire des Polynomes de Kazhdan-Lusztig sur les intervalles partant de l'origine
• Combinatorial invariance for Kazhdan-Lusztig R-polynomials of elementary intervals