Congruence B-orbits and the Bruhat poset of involutions of the symmetric group

Eli Bagno; Yonah Cherniavsky

doi:10.1016/j.disc.2011.12.018

Congruence B-orbits and the Bruhat poset of involutions of the symmetric group

Eli Bagno, Yonah Cherniavsky

Department of Mathematics

Ariel University

Research output: Contribution to journal › Article › peer-review

Abstract

We study the poset of Borel congruence classes of symmetric matrices ordered by containment of closures. We give a combinatorial description of this poset and calculate its rank function. We discuss the relation between this poset and the Bruhat poset of involutions of the symmetric group.

Original language	English
Pages (from-to)	1289-1299
Number of pages	11
Journal	Discrete Mathematics
Volume	312
Issue number	6
DOIs	https://doi.org/10.1016/j.disc.2011.12.018
State	Published - 28 Mar 2012

Keywords

Bruhat poset
Involutions of the symmetric group
Partial permutations

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2011.12.018

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title = "Congruence B-orbits and the Bruhat poset of involutions of the symmetric group",

abstract = "We study the poset of Borel congruence classes of symmetric matrices ordered by containment of closures. We give a combinatorial description of this poset and calculate its rank function. We discuss the relation between this poset and the Bruhat poset of involutions of the symmetric group.",

keywords = "Bruhat poset, Involutions of the symmetric group, Partial permutations",

author = "Eli Bagno and Yonah Cherniavsky",

note = "Funding Information: The second author was also supported by the Swiss National Science Foundation , 2009. Funding Information: It is a pleasure for us to thank Dr. Anna Melnikov, whose work [5] gave the starting point for this paper. We are grateful to Prof. Ron Adin for many helpful discussions. We would like to express a special gratitude to Prof. Lex Renner for providing us very useful information about the Bruhat poset and for answering our questions. Also, we are grateful to Prof. Yuval Roichman and to Prof. Uzi Vishne for helpful discussions. The second author would like to thank the Faculty of Mathematics, Technion, Israel, and the Department of Mathematics, University of Geneva, Switzerland, for the hospitality and for the financial support.",

year = "2012",

month = mar,

day = "28",

doi = "10.1016/j.disc.2011.12.018",

language = "الإنجليزيّة",

volume = "312",

pages = "1289--1299",

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T1 - Congruence B-orbits and the Bruhat poset of involutions of the symmetric group

AU - Bagno, Eli

AU - Cherniavsky, Yonah

N1 - Funding Information: The second author was also supported by the Swiss National Science Foundation , 2009. Funding Information: It is a pleasure for us to thank Dr. Anna Melnikov, whose work [5] gave the starting point for this paper. We are grateful to Prof. Ron Adin for many helpful discussions. We would like to express a special gratitude to Prof. Lex Renner for providing us very useful information about the Bruhat poset and for answering our questions. Also, we are grateful to Prof. Yuval Roichman and to Prof. Uzi Vishne for helpful discussions. The second author would like to thank the Faculty of Mathematics, Technion, Israel, and the Department of Mathematics, University of Geneva, Switzerland, for the hospitality and for the financial support.

PY - 2012/3/28

Y1 - 2012/3/28

N2 - We study the poset of Borel congruence classes of symmetric matrices ordered by containment of closures. We give a combinatorial description of this poset and calculate its rank function. We discuss the relation between this poset and the Bruhat poset of involutions of the symmetric group.

AB - We study the poset of Borel congruence classes of symmetric matrices ordered by containment of closures. We give a combinatorial description of this poset and calculate its rank function. We discuss the relation between this poset and the Bruhat poset of involutions of the symmetric group.

KW - Bruhat poset

KW - Involutions of the symmetric group

KW - Partial permutations

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U2 - 10.1016/j.disc.2011.12.018

DO - 10.1016/j.disc.2011.12.018

M3 - مقالة

SN - 0012-365X

VL - 312

SP - 1289

EP - 1299

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 6

ER -

Congruence B-orbits and the Bruhat poset of involutions of the symmetric group

Abstract

Keywords

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