A symmetrical presentation for the singular part of the symmetric inverse monoid

James East

doi:10.1007/s00012-015-0347-y

A symmetrical presentation for the singular part of the symmetric inverse monoid

James East

School of Computer, Data & Mathematical Sciences

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

9 Citations (Scopus)

Abstract

We give a presentation for In Sn, the semigroup of all singular injective partial transformations on an n-element set, in terms of a particularly symmetrical generating set. Our generators are all restrictions of transpositions, and the relations we obtain display all the symmetry possessed by In Sn.

Original language	English
Pages (from-to)	207-228
Number of pages	22
Journal	Algebra Universalis
Volume	74
Issue number	3
DOIs	https://doi.org/10.1007/s00012-015-0347-y
Publication status	Published - 2015

Keywords

coxeter groups
inverse semigroups
monoids
semigroups
symmetry

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10.1007/s00012-015-0347-y

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AB - We give a presentation for In Sn, the semigroup of all singular injective partial transformations on an n-element set, in terms of a particularly symmetrical generating set. Our generators are all restrictions of transpositions, and the relations we obtain display all the symmetry possessed by In Sn.

KW - coxeter groups

KW - inverse semigroups

KW - monoids

KW - semigroups

KW - symmetry

UR - http://handle.uws.edu.au:8081/1959.7/uws:31737

U2 - 10.1007/s00012-015-0347-y

DO - 10.1007/s00012-015-0347-y

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VL - 74

SP - 207

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JO - Algebra Universalis

JF - Algebra Universalis

IS - 3

ER -

A symmetrical presentation for the singular part of the symmetric inverse monoid

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Keywords

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