Largest 2-generated subsemigroups of the symmetric inverse semigroup

J. M. Andre; V. H. Fernandes; J. D. Mitchell

doi:10.1017/S0013091505001598

Largest 2-generated subsemigroups of the symmetric inverse semigroup

J. M. Andre, V. H. Fernandes, J. D. Mitchell

Research output: Contribution to journal › Article › peer-review

Abstract

The symmetric inverse monoid I-n,, is the set of all partial permutations of an n-element set. The largest possible size of a 2-generated subsemigroup of I-n is determined. Examples of semigroups with these sizes are given. Consequently, if M(n) denotes this maximum, it is shown that M(n)vertical bar I-n vertical bar -> 1 as n -> infinity. Furthermore, we deduce the known fact that I-n embeds as a local submonoid of an inverse 2-generated subsemigroup of In+1.

Original language	English
Pages (from-to)	551-561
Number of pages	11
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	50
DOIs	https://doi.org/10.1017/S0013091505001598
Publication status	Published - Oct 2007

Keywords

inverse semigroups
generators
subsemigroups

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10.1017/S0013091505001598

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abstract = "The symmetric inverse monoid I-n,, is the set of all partial permutations of an n-element set. The largest possible size of a 2-generated subsemigroup of I-n is determined. Examples of semigroups with these sizes are given. Consequently, if M(n) denotes this maximum, it is shown that M(n)vertical bar I-n vertical bar -> 1 as n -> infinity. Furthermore, we deduce the known fact that I-n embeds as a local submonoid of an inverse 2-generated subsemigroup of In+1.",

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AB - The symmetric inverse monoid I-n,, is the set of all partial permutations of an n-element set. The largest possible size of a 2-generated subsemigroup of I-n is determined. Examples of semigroups with these sizes are given. Consequently, if M(n) denotes this maximum, it is shown that M(n)vertical bar I-n vertical bar -> 1 as n -> infinity. Furthermore, we deduce the known fact that I-n embeds as a local submonoid of an inverse 2-generated subsemigroup of In+1.

KW - inverse semigroups

KW - generators

KW - subsemigroups

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EP - 561

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

ER -

Largest 2-generated subsemigroups of the symmetric inverse semigroup

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