1 1 Ju n 20 01 EXPLICIT ENUMERATION OF 321 , HEXAGON – AVOIDING PERMUTATIONS

The 321,hexagon–avoiding (321–hex) permutations were introduced and studied by Billey and Warrington in [4] as a class of elements of Sn whose Kazhdan– Lusztig and Poincaré 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.