Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations
| dc.creator | Billey, Sara C. | |
| dc.creator | Warrington, Gregory S. | |
| dc.date | 2000-05-05 | |
| dc.date.accessioned | 2026-07-07T04:35:02Z | |
| dc.date.available | 2026-07-07T04:35:02Z | |
| dc.description | We give a combinatorial formula for the Kazhdan-Lusztig polynomials $P_{x,w}$ in the symmetric group when $w$ is a 321-hexagon-avoiding permutation. Our formula, which depends on a combinatorial framework developed by Deodhar, can be expressed in terms of a simple statistic on all subexpressions of any fixed reduced expression for $w$. We also show that $w$ being 321-hexagon-avoiding is equivalent to several other conditions, such as the Bott-Samelson resolution of the Schubert variety $X_w$ being small. We conclude with a simple method for completely determining the singular locus of $X_w$ when $w$ is 321-hexagon-avoiding. | |
| dc.description | 24 pages, 18 figures, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0005052 | |
| dc.identifier | http://arxiv.org/abs/math/0005052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59130 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E15 (Primary) 20F55, 32S45, 14M15 (Secondary) | |
| dc.title | Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations | |
| dc.type | text |