%0 Journal Article
%T Explicit Enumeration of 321,Hexagon-Avoiding Permutations
%A Zvezdelina Stankova-Frenkel
%A Julian West
%J Mathematics
%D 2001
%I arXiv
%X The 321,hexagon-avoiding (321-hex) permutations were introduced and studied by Billey and Warrington in as a class of elements of S_n whose Kazhdan-Lusztig and Poincare polynomials and the singular loci of whose Schubert varieties have certain fairly simple and explicit descriptions. This paper provides a 7-term linear recurrence relation leading to an explicit enumeration of the 321-hex permutations. A complete description of the corresponding generating tree is obtained as a by-product of enumeration techniques used in the paper, including Schensted's 321-subsequences decomposition, a 5-parameter generating function and the symmetries of the octagonal patterns avoided by the 321-hex permutations.
%U http://arxiv.org/abs/math/0106073v1