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Ranks of ideals in inverse semigroups of difunctional binary relations

East, James and Vernitski, Alexei (2018) 'Ranks of ideals in inverse semigroups of difunctional binary relations.' Semigroup Forum, 96 (1). 21 - 30. ISSN 0037-1912

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The set Dn of all difunctional relations on an n element set is an inverse semigroup under a variation of the usual composition operation. We solve an open problem of Kudryavtseva and Maltcev (Publ Math Debrecen 78(2):253–282, 2011), which asks: What is the rank (smallest size of a generating set) of Dn? Specifically, we show that the rank of Dn is B(n)+n, where B(n) is the nth Bell number. We also give the rank of an arbitrary ideal of Dn. Although Dn bears many similarities with families such as the full transformation semigroups and symmetric inverse semigroups (all contain the symmetric group and have a chain of J-classes), we note that the fast growth of rank(Dn) as a function of n is a property not shared with these other families.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 09 Jan 2017 10:53
Last Modified: 25 Sep 2018 14:15

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