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Discrete Mathematics & Theoretical Computer Science
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Avoiding maximal parabolic subgroups of S_k

Avoiding maximal parabolic subgroups of \(S_k\)
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2000Embargo end date: 01 Jan 2000 English Publisher:Centre pour la Communication Scientifique Directe (CCSD)Journal:Discrete Mathematics & Theoretical Computer Science, volume Vol. 4 no. 1 (eissn: 1365-8050, Copyright policy )
Authors: Mansour, Toufik; Vainshtein, Alek;

doi: 10.46298/dmtcs.276 , 10.48550/arxiv.math/0006164

arXiv: math/0006164

Avoiding maximal parabolic subgroups of S_k

Abstract

We find an explicit expression for the generating function of the number of permutations in S_n avoiding a subgroup of S_k generated by all but one simple transpositions. The generating function turns out to be rational, and its denominator is a rook polynomial for a rectangular board.

Related Organizations
Keywords

permutations, Exact enumeration problems, generating functions, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], rook polynomial, parabolic subgroups, permutation, 05A05, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, Laguerre polynomials, Symmetric groups, laguerre polynomials, 05A05; 05A15; 05E35; 33C45, rook polynomials, 33C45, forbidden patterns, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], 05E35, generating function, Combinatorics (math.CO), 05A15, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
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Average
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