On involutions of the symmetric group and congruence b-orbits of anti-symmetric matrices

Yonah Cherniavsky

doi:10.1142/S0218196711006546

On involutions of the symmetric group and congruence b-orbits of anti-symmetric matrices

Yonah Cherniavsky

Department of Mathematics

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

12 Scopus citations

Abstract

We present the poset of Borel congruence classes of anti-symmetric matrices ordered by containment of closures. We show that there exists a bijection between the set of these classes and the set of involutions of the symmetric group. We give two formulas for the rank function of this poset.

Original language	English
Pages (from-to)	841-856
Number of pages	16
Journal	International Journal of Algebra and Computation
Volume	21
Issue number	5
DOIs	https://doi.org/10.1142/S0218196711006546
State	Published - Aug 2011

Keywords

Involutions of the symmetric group
anti-symmetric matrices
congruence B-orbits
poset of matrix varieties

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10.1142/S0218196711006546

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title = "On involutions of the symmetric group and congruence b-orbits of anti-symmetric matrices",

abstract = "We present the poset of Borel congruence classes of anti-symmetric matrices ordered by containment of closures. We show that there exists a bijection between the set of these classes and the set of involutions of the symmetric group. We give two formulas for the rank function of this poset.",

keywords = "Involutions of the symmetric group, anti-symmetric matrices, congruence B-orbits, poset of matrix varieties",

author = "Yonah Cherniavsky",

note = "Funding Information: ∗The author was supported by the Swiss National Science Foundation. Funding Information: I would like to express the special gratitude to Prof. Lex Renner for the very useful information about the Bruhat poset and answering the numerous questions. This work was done when I was a postdoc at the Department of Mathematics at the University of Geneva and I would like to thank the department and especially Prof. Tatiana Smirnova-Nagnibeda for the hospitality and discussion. I am grateful to the Swiss National Science Foundation for the financial support. I am grateful to Prof. Ron M. Adin, Dr. Eli Bagno, Dr. Anna Melnikov, Prof. Yuval Roichman and Prof. Uzi Vishne for the helpful discussions.",

year = "2011",

month = aug,

doi = "10.1142/S0218196711006546",

language = "אנגלית",

volume = "21",

pages = "841--856",

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AU - Cherniavsky, Yonah

N1 - Funding Information: ∗The author was supported by the Swiss National Science Foundation. Funding Information: I would like to express the special gratitude to Prof. Lex Renner for the very useful information about the Bruhat poset and answering the numerous questions. This work was done when I was a postdoc at the Department of Mathematics at the University of Geneva and I would like to thank the department and especially Prof. Tatiana Smirnova-Nagnibeda for the hospitality and discussion. I am grateful to the Swiss National Science Foundation for the financial support. I am grateful to Prof. Ron M. Adin, Dr. Eli Bagno, Dr. Anna Melnikov, Prof. Yuval Roichman and Prof. Uzi Vishne for the helpful discussions.

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N2 - We present the poset of Borel congruence classes of anti-symmetric matrices ordered by containment of closures. We show that there exists a bijection between the set of these classes and the set of involutions of the symmetric group. We give two formulas for the rank function of this poset.

AB - We present the poset of Borel congruence classes of anti-symmetric matrices ordered by containment of closures. We show that there exists a bijection between the set of these classes and the set of involutions of the symmetric group. We give two formulas for the rank function of this poset.

KW - Involutions of the symmetric group

KW - anti-symmetric matrices

KW - congruence B-orbits

KW - poset of matrix varieties

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SN - 0218-1967

VL - 21

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JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 5

ER -

On involutions of the symmetric group and congruence b-orbits of anti-symmetric matrices

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Keywords

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