Generators and relations for partition monoids and algebras

We investigate the manner in which the partition monoid P(n) and algebra P(n)(xi) may be presented by generators and relations. Making use of structural properties of P(n), as well as presentations for several key submonoids, we obtain a number of presentations for P(n), 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 P(n)(xi). (C) 2011 Elsevier Inc. All rights reserved.