Séminaire Lotharingien de Combinatoire, 91B.7 (2024), 12 pp.
Christian Gaetz and Yibo Gao
Pattern Heights and The Minimal Power of q in a Kazhdan-Lusztig Polynomial
Abstract.
For w in the symmetric group, we use permutation patterns to provide
an exact formula for the smallest positive
power qh(w) appearing in the Kazhdan-Lusztig
polynomial Pe,w(q).
We also use Weyl group
patterns to provide a tight upper bound on h(w) in simply-laced
types, resolving a conjecture of Billey-Postnikov from 2002.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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