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Algebra Discrete Math., 2016, Volume 21, Issue 1, Pages 1–17 (Mi adm550)  

RESEARCH ARTICLE

Classification of $\mathscr{L}$-cross-sections of the finite symmetric semigroup up to isomorphism

Eugenija Bondarab

a Luhansk Taras Shevchenko National University
b Ural Federal University

Abstract: Let $\mathscr{T}_n$ be the symmetric semigroup of full transformations on a finite set with $n$ elements. In the paper we give a counting formula for the number of $\mathscr{L}$-cross-sections of $\mathscr{T}_n$ and classify all $\mathscr{L}$-cross-sections of $\mathscr{T}_n$ up to isomorphism.

Keywords: symmetric semigroup, cross-section, Green's relations.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.1999.2014/K
Ural Federal University named after the First President of Russia B. N. Yeltsin
The author acknowledges support from the Ministry of Education and Science of the Russian Federation, project no. 1.1999.2014/K, and the Competitiveness Program of Ural Federal University.


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Bibliographic databases:
MSC: 20M20
Received: 04.06.2014
Revised: 08.10.2015
Language:

Citation: Eugenija Bondar, “Classification of $\mathscr{L}$-cross-sections of the finite symmetric semigroup up to isomorphism”, Algebra Discrete Math., 21:1 (2016), 1–17

Citation in format AMSBIB
\Bibitem{Bon16}
\by Eugenija~Bondar
\paper Classification of $\mathscr{L}$-cross-sections of the finite symmetric semigroup up to isomorphism
\jour Algebra Discrete Math.
\yr 2016
\vol 21
\issue 1
\pages 1--17
\mathnet{http://mi.mathnet.ru/adm550}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3537481}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000382847600002}


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