Abstract
We study the singular part of the partition monoid [Formula: see text]; that is, the ideal [Formula: see text], where [Formula: see text] is the symmetric group. Our main results are presentations in terms of generators and relations. We also show that [Formula: see text] is idempotent generated, and that its rank and idempotent-rank are both equal to [Formula: see text]. One of our presentations uses an idempotent generating set of this minimal cardinality.
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