321-avoiding affine permutations and their many heaps
نویسندگان
چکیده
منابع مشابه
On 321-Avoiding Permutations in Affine Weyl Groups
We introduce the notion of 321-avoiding permutations in the affine Weyl group W of type An−1 by considering the group as a George group (in the sense of Eriksson and Eriksson). This enables us to generalize a result of Billey, Jockusch and Stanley to show that the 321-avoiding permutations in W coincide with the set of fully commutative elements; in other words, any two reduced expressions for ...
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 کامل321-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]...
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...
متن کاملInversion Formulae on Permutations Avoiding 321
We will study the inversion statistic of 321-avoiding permutations, and obtain that the number of 321-avoiding permutations on [n] with m inversions is given by
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2019
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2018.11.002