$321$-Polygon-Avoiding Permutations and Chebyshev Polynomials
نویسندگان
چکیده
منابع مشابه
321-Polygon-Avoiding Permutations and Chebyshev Polynomials
A 321-k-gon-avoiding permutation π avoids 321 and the following four patterns: k(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · (k − 1)(k + 1), k(k + 2)(k + 3) · · · (2k − 1)(2k)12 · · · (k − 1)(k + 1), (k + 1)(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · k, (k + 1)(k + 2)(k + 3) · · · (2k − 1)(2k)123 · · · k. The 321-4-gon-avoiding permutations were introduced and studied by Billey and Warrington [BW]...
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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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This addendum contains results about the inversion number and major index polynomials for permutations avoiding 321 which did not fit well into the original paper. In particular, we consider symmetry, unimodality, behavior modulo 2, and signed enumeration.
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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 ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2003
ISSN: 1077-8926
DOI: 10.37236/1677