A224316 Number of permutations w in S_n whose Kazhdan-Lusztig polynomial P_{id,w}(1) <= 3.

1, 2, 6, 24, 119, 654, 3622

Offset

1,2

Comments

This family of permutations is closed under taking patterns. It is conjectured to be characterized by a finite set of patterns by Billey and Weed.

References

S. Billey and T. Braden, Lower bounds for Kazhdan-Lusztig polynomials from patterns} (with Tom Braden). Transform. Groups 8 (2003), no. 4, 321-332.

Links

Table of n, a(n) for n=1..7.

FindStat - Combinatorial Statistic Finder, The evaluation of the Kazhdan-Lusztig polynomial P(id,w) for each permutation w in S_n evaluated at q = 1

A. Woo, Permutations with Kazhdan-Lusztig polynomial P_{id,w}(q) = 1 + q^h with appendix by Sara Billey and Jonathan Weed, The Electronic Journal of Combinatorics, Volume 16(2), 2009.

Crossrefs

Cf. A224255.

Sequence in context: A005394 A095818 A264781 * A256195 A256196 A256197

Adjacent sequences: A224313 A224314 A224315 * A224317 A224318 A224319

Keyword

nonn,more

Author

Sara Billey, Apr 03 2013

Status

approved