Explicit enumeration of 321, hexagon-avoiding permutations
نویسندگان
چکیده
منابع مشابه
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 pe...
متن کامل1 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 pe...
متن کاملKazhdan-Lusztig Polynomials for 321-Hexagon-Avoiding Permutations
In (Deodhar, Geom. Dedicata, 36(1) (1990), 95–119), Deodhar proposes a combinatorial framework for determining the Kazhdan-Lusztig polynomials Px,w in the case where W is any Coxeter group. We explicitly describe the combinatorics in the case where W = Sn (the symmetric group on n letters) and the permutation w is 321-hexagon-avoiding. Our formula can be expressed in terms of a simple statistic...
متن کاملThe Fine Structure of 321 Avoiding Permutations. the Fine Structure of 321 Avoiding Permutations
Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in enumerating permutations which have a block structure avoiding 321, and whose blocks also have such structure (recursively). Generalizations of these results ...
متن کاملInversion polynomials for 321-avoiding permutations
We prove a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor giving a recursion for the inversion polynomial of 321-avoiding permutations. We also answer a question they posed about finding a recursive formulas for the major index polynomial of 321-avoiding permutations. Other properties of these polynomials are investigated as well. Our tools include Dyck and 2-Motzkin...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/j.disc.2003.06.003