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

• Datum: 2016
• 1. Verfasser: Bondar, Eugenija
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2016
• Schlagworte: symmetric semigroup; cross-section; Green's relations; 20M20
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/28
• Назва журналу: Algebra and Discrete Mathematics

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 isomor...