The Eulerian Distribution on the Involutions of the Hyperoctahedral Group is Unimodal

被引：6

作者：

Moustakas, Vassilis-Dionyssis ^{[1
]}

机构：

[1] Univ Athens, Athens 15784, Greece

来源：

GRAPHS AND COMBINATORICS | 2019年 / 35卷 / 05期

关键词：

Involution; Descent; Unimodality; Hyperoctahedral group; Quasisymmetric function;

D O I：

10.1007/s00373-019-02058-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Eulerian distribution on the involutions of the symmetric group is unimodal, as shown by Guo and Zeng. In this paper we prove that the Eulerian distribution on the involutions of the hyperoctahedral group, when viewed as a colored permutation group, is unimodal in a similar way and we compute its generating function, using signed quasisymmetric functions.

引用

页码：1077 / 1090

页数：14

共 19 条

[1] Character formulas descents for the hyperoctahedral group [J].

Adin, Ron M. ;

Athanasiadis, Christos A. ;

Elizalde, Sergi ;

Roichman, Yuval .

ADVANCES IN APPLIED MATHEMATICS, 2017, 87 :128-169

[2] Descent numbers and major indices for the hyperoctahedral group [J].

Adinh, RM ;

Brenti, F ;

Roichman, Y .

ADVANCES IN APPLIED MATHEMATICS, 2001, 27 (2-3) :210-224

[3]

Athanasiadis C.A., 2018, Semin. Lothar. Comb., V77, pB77i

[4] The descent statistic on involutions is not log-concave [J].

Barnabei, Marilena ;

Bonetti, Flavio ;

Silimbani, Matteo .

EUROPEAN JOURNAL OF COMBINATORICS, 2009, 30 (01) :11-16

[5]

Barnabei M, 2009, DISCRETE MATH THEOR, V11, P95

[6]

BJORNER A, 2005, GRAD TEXT M, V231

[7]

Branden P., 2015, HDB ENUMERATIVE COMB, V87, P437

[8]

DESARMENIEN J, 1985, B SOC MATH FR, V113, P3

[9] Permutation statistics on involutions [J].

Dukes, W. M. B. .

EUROPEAN JOURNAL OF COMBINATORICS, 2007, 28 (01) :186-198

[10]

Foata D., 1970, LECT NOTES MATH, V138

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