Excedance Numbers for the Permutations of Type B

Zhao, Alina F. Y.

doi:10.37236/2375

Cited by 4 publications

(3 citation statements)

References 12 publications

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“…There is a large of literature devoted to various generalizations and refinements of the joint distribution of excedances and cycles, see, e.g. [12,15,19] and the references therein. Define A n (x, y, q) = π∈Sn…”

Section: Multivariable Binomial-eulerian Polynomialsmentioning

confidence: 99%

Recurrence relations for binomial-Eulerian polynomials

Ma,

Yeh

2017

Preprint

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Binomial-Eulerian polynomials were introduced by Postnikov, Reiner and Williams.In this paper, properties of the binomial-Eulerian polynomials, including recurrence relations and generating functions are studied. We present three constructive proofs of the recurrence relations for binomial-Eulerian polynomials. Moreover, we give a combinatorial interpretation of the Betti number of the complement of the k-equal real hyperplane arrangement.

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Section: Multivariable Binomial-eulerian Polynomialsmentioning

confidence: 99%

Recurrence relations for binomial-Eulerian polynomials

Ma,

Yeh

2017

Preprint

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“…For fixed r, the exponential generating function of these permutations was computed in [31,Theorem 39]. The following statement specializes to [34,Theorem 11] for r = 2. 3.…”

Section: Subdivisionsmentioning

confidence: 99%

Edgewise Subdivisions, Local $h$-Polynomials, and Excedances in the Wreath Product $\mathbb{Z}_r \wr \mathfrak{S}_n$

Athanasiadis¹

2014

SIAM J. Discrete Math.

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The coefficients of the local h-polynomial of the barycentric subdivision of the simplex with n vertices are known to count derangements in the symmetric group S n by the number of excedances. A generalization of this interpretation is given for the local h-polynomial of the rth edgewise subdivision of the barycentric subdivision of the simplex. This polynomial is shown to be γ-nonnegative and a combinatorial interpretation to the corresponding γ-coefficients is provided. The new combinatorial interpretations involve the notions of flag excedance and descent in the wreath product Z r ≀ S n . A related result on the derangement polynomial for Z r ≀ S n , studied by Chow and Mansour, is also derived from results of Linusson, Shareshian and Wachs on the homology of Rees products of posets.

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“…From then on, there is a large of literature devoted to various generalizations and refinements of the joint distribution of excedances and cycles (see [1,5,8,14] for instance). For example, Ksavrelof and Zeng [8] constructed bijective proofs of 1 and the following formula:…”

Section: Introductionmentioning

confidence: 99%