Generators and relations for partition monoids and algebras

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