@article{3c7fa29a32be41bb9c345aa22ae617b6,
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",
journal = "International Journal of Algebra and Computation",
issn = "0218-1967",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "5",
}