The monoid of ordered partitions of a natural number

DOI10.1007/BF02574119zbMath0852.20050MaRDI QIDQ1916037

T. G. Lavers

Publication date: 1996

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/135468

zbMATH Keywords

presentationalgorithmleft idealsHasse diagramordered partitionspositive integersmonoid of partial finite-to-one order-preserving transformationsposet of left principal idealsposets of principal one-sided idealssequences of nonnegative integers

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Ideal theory for semigroups (20M12) Semigroups of transformations, relations, partitions, etc. (20M20) Free semigroups, generators and relations, word problems (20M05) Combinatorics of partially ordered sets (06A07) Elementary theory of partitions (11P81)

Related Items (5)

Ranks of Semigroups Generated by Order-Preserving Transformations with a Fixed Partition Type ⋮ Semigroup theory of symmetry ⋮ The theory of vines ⋮ The monoid of all injective orientation preserving partial transformations on a finite chain ⋮ Regular order-preserving transformation semigroups

Cites Work

• Enumerating nested and consecutive partitions
• Catalan monoids, monoids of local endomorphisms, and their presentations
• DIVISORS OF SEMIGROUPS OF ORDER-PRESERVING MAPPINGS ON A FINITE CHAIN
• Combinatorial results for semigroups of order-preserving mappings
• Products of idempotents in certain semigroups of transformations
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