Largest subsemigroups of the full transformation monoid.
type: Item
instance of: scholarly article
title: Largest subsemigroups of the full transformation monoid.
zbMATH Open document ID: 1152.20052
published in: Discrete Mathematics
publication date: 2008-09-04T00:00:00Z
review text: Let \(T_n\) denote the full transformation semigroup on an \(n\)-element set. In the paper under review the authors prove the following main results: (1) The largest size of a left zero subsemigroup of \(T_n\) is \(3^{(n/3)}\) if \(3\mid n\); \(4\cdot 3^{(n-4)/3}\) if \(3\mid n-1\); and \(2\cdot 3^{(n-2)/3}\) if \(3\mid n-2\). (2) The largest completely simple subsemigroup of \(T_n\) is the symmetric group \(S_n\). (3) The largest size of an inverse subsemigroup of \(T_n\) is \(\sum_{m=0}^{n-1}\binom{n-1}{m}^2m!\). Example of largest size subsemigroups are given.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 5321354
zbMATH Keywords: maximal subsemigroups
zbMATH Keywords: full transformation semigroups
zbMATH Keywords: left zero semigroups
zbMATH Keywords: completely simple semigroups
zbMATH Keywords: inverse semigroups
author: R. Gray
author: J. D. Mitchell
MaRDI profile type: Publication
full work available at URL: j.disc.2007.08.075
OpenAlex ID: W2005189683
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DOI: 10.1016/J.DISC.2007.08.075
description: scientific article; zbMATH DE number 5321354