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The \(\gamma \)-positive coefficients arising in segmented permutations. (English) Zbl 1476.05008

Summary: The \(\gamma \)-coefficients of Eulerian polynomials were first considered by D. Foata and M. P. Schützenberger [Théorie géométrique des polynômes eulériens. Berlin-Heidelberg-New York: Springer-Verlag (1970; Zbl 0214.26202)]. In this paper, we provide combinatorial interpretations for the \(\gamma \)-coefficients arising from the segmented permutations and segmented derangements via Brändén’s modified Foata-Strehl action. We also give the combinatorial interpretations of \(\gamma \)-coefficients for the \(( > , \leq , - )\)-avoiding inversion sequences via continued fractions.

MSC:

05A05 Permutations, words, matrices
05A15 Exact enumeration problems, generating functions
05A19 Combinatorial identities, bijective combinatorics
11B68 Bernoulli and Euler numbers and polynomials

Citations:

Zbl 0214.26202

Software:

OEIS
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Full Text: DOI

References:

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