Fixed points of 321-avoiding permutations

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The 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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Inversion 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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The fine structure of 321 avoiding permutations

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Inversion Formulae on Permutations Avoiding 321

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Inversion polynomials for 321-avoiding permutations: addendum

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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ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 2018

ISSN: 0002-9939,1088-6826

DOI: 10.1090/proc/14299