Generators and relations for partition monoids and algebras

James East

doi:10.1016/j.jalgebra.2011.04.008

Generators and relations for partition monoids and algebras

James East

School of Computer, Data & Mathematical Sciences

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

58 Citations (Scopus)

Abstract

We investigate the manner in which the partition monoid Pn and algebra PÎ¾ 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 PnÎ¾ .

Original language	English
Pages (from-to)	1-26
Number of pages	26
Journal	Journal of Algebra
Volume	339
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2011.04.008
Publication status	Published - 2011

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10.1016/j.jalgebra.2011.04.008

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title = "Generators and relations for partition monoids and algebras",

abstract = "We investigate the manner in which the partition monoid Pn and algebra P{\^I}¾ 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 Pn{\^I}¾ .",

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AB - We investigate the manner in which the partition monoid Pn and algebra PÎ¾ 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 PnÎ¾ .

UR - http://handle.uws.edu.au:8081/1959.7/540061

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DO - 10.1016/j.jalgebra.2011.04.008

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JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

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Generators and relations for partition monoids and algebras

Abstract

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