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arXiv · 2606.11776

Special Matchings, Brenti's Conjecture, and the Combinatorial Invariance Conjecture

Fabrizio Caselli·Mario Marietti
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Abstract

In this work, we settle a problem that dates back to the early 2000s. We provide a complete characterization of special matchings of arbitrary Bruhat intervals in Coxeter groups of type $A$ and apply this result to prove a conjecture of Brenti from 2003 concerning the computation of Kazhdan-Lusztig $R$-polynomials via special matchings. This yields new evidence in support of the Combinatorial Invariance Conjecture.

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Fabrizio Caselli, Mario Marietti. 2026-06-10. Special Matchings, Brenti's Conjecture, and the Combinatorial Invariance Conjecture. https://arxiv.org/abs/2606.11776

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