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

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    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 languageEnglish
    Pages (from-to)207-228
    Number of pages22
    JournalAlgebra Universalis
    Volume74
    Issue number3
    DOIs
    Publication statusPublished - 2015

    Keywords

    • coxeter groups
    • inverse semigroups
    • monoids
    • semigroups
    • symmetry

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