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Journal ArticleDOI

Counting derangements, involutions and unimodal elements in the wreath product Cr ≀ Sn

Chak-On Chow, +1 more
- 31 Oct 2010 - 
- Vol. 179, Iss: 1, pp 425-448
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TLDR
In this article, the authors count derangements, involutions and unimodal elements in the wreath product Cr ≀ Sn by the numbers of excedances, fixed points and 2-cycles.
Abstract: 
We count derangements, involutions and unimodal elements in the wreath product Cr ≀ Sn by the numbers of excedances, fixed points and 2-cycles. Properties of the generating functions, including combinatorial formulas, recurrence relations and real-rootedness are studied. The results obtained specialize to those on the symmetric group Sn and on the hyperoctahedral group Bn when r = 1, 2, respectively.

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Gamma-positivity in combinatorics and geometry

Christos A. Athanasiadis
- 16 Nov 2017 - 
TL;DR: Gamma-positivity is an elementary property that polynomials with symmetric coefficients may have, which directly implies their unimodality as mentioned in this paper, and has found numerous applications since then.
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Symmetric Decompositions and Real-Rootedness

Petter Brändén, +1 more
- 21 May 2021 - 
TL;DR: In this article, the alternatingly increasing property of polynomials has been studied in algebraic, topological, and geometric combinatorics inequalities among the coefficients of combinatorial polynomial coefficients.
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Edgewise subdivisions, local h-polynomials and excedances in the wreath product Z r ≀S n

Christos A. Athanasiadis
TL;DR: In this paper, a generalization of this interpretation is given for the local h-polynomial of the rth edgewise subdivision of the barycentric subdivision of a simplex with n vertices.
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A survey of subdivisions and local $h$-vectors

Christos A. Athanasiadis
- 27 Mar 2014 - 
TL;DR: The enumerative theory of simplicial subdivisions (triangulations) was developed by Stanley in order to understand the effect of such subdivisions on the $h$-vector of a simplicial complex as mentioned in this paper.
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Symmetric unimodal expansions of excedances in colored permutations

Heesung Shin, +1 more
- 01 Feb 2016 - 
TL;DR: In this article, several generalizations of the classical γ -positivity of Eulerian polynomials (and their derangement analogues) using generating functions and combinatorial theory of continued fractions were considered.
References
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Book

Methods of Mathematical Physics

Richard Courant, +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Book

Enumerative Combinatorics

R P Stanley
Book

Enumerative Combinatorics

Charalambos A. Charalambides
TL;DR: This review of 3 Enumerative Combinatorics, by Charalambos A.good, does not support this; the label ‘Example’ is given in a rather small font followed by a ‘PROOF,’ and the body of an example is nonitalic, utterly unlike other statements accompanied by demonstrations.
Book

Unimodal Log Concave and Polya Frequency Sequences in Combinatorics

Francesco Brenti
TL;DR: In this article, the authors affine affiner ces deux notions for definir les suites de frequences de Polya which possedent des proprietes plus convenables.
Book

Theorie Geometrique des Polynomes Euleriens

Dominique Foata, +1 more