Explicit Enumeration of 321,Hexagon-Avoiding Permutations

Details Explicit Enumeration of 321,Hexagon-Avoiding Permutations Explicit Enumeration of 321,Hexagon-Avoiding Permutations

2001-06-11

arxiv.org/abs/math/0106073v1

Mathematics

Combinatorics

21 pages, 12 figures. submitted to Discrete Mathematics

Scientific paper

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.

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