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Presentations for rook partition monoids and algebras and their singular ideals. (English) Zbl 1499.20126

Summary: We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals. Among other results, we also calculate the minimal sizes of generating sets (some of our presentations use such minimal-size generating sets), and show that the singular part of the rook partition monoid is generated by its idempotents.

MSC:

20M05 Free semigroups, generators and relations, word problems
20M20 Semigroups of transformations, relations, partitions, etc.
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