Generators and relations for partition monoids and algebras

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    Abstract

    We investigate the manner in which the partition monoid Pn and algebra Pξ n may be presented by generators and relations. Making use of structural properties of Pn, as well as presentations for several key submonoids, we obtain a number of presentations for Pn, including that given (without a complete proof) by Halverson and Ram in 2005. We then conclude by showing how each of these presentations gives rise to an algebra presentation for Pnξ .
    Original languageEnglish
    Pages (from-to)1-26
    Number of pages26
    JournalJournal of Algebra
    Volume339
    Issue number1
    DOIs
    Publication statusPublished - 2011

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