On the semigroups of order-decreasing finite full transformations

DOI10.1017/S0308210500015031zbMath0746.20048MaRDI QIDQ3991038

Abdullahi Umar

Publication date: 28 June 1992

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

Green's relationsnilpotent elementsStirling numbersidempotent rankfinite monoidgenerated by idempotentsBell's exponential numbersincreasing singular mapssingular, order decreasing maps

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Semigroups of transformations, relations, partitions, etc. (20M20)

Related Items (33)

Combinatorial results for semigroups of order-preserving partial transformations. ⋮ The monoid of orientation-preserving \(k\)-extensive transformations ⋮ Abundance of the ideals of the order-preserving and decreasing full transformation semigroup ⋮ The ideals of the monoid of all partial order-preserving extensive transformations ⋮ On the semigroups of partial one-to-one order-decreasing finite transformations ⋮ The monoid of all orientation-preserving and extensive full transformations on a finite chain ⋮ Remarks on isomorphisms of regressive transformation semigroups ⋮ Semigroups of order-decreasing transformations: The isomorphism theorem ⋮ A proof of Simon's theorem on piecewise testable languages ⋮ The monoid of all orientation-preserving and extensive partial transformations on a finite chain ⋮ Automorphisms of partition order-decreasing transformation monoids. ⋮ Combinatorial results for semigroups of orientation-preserving and order-decreasing transformations ⋮ A natural partial order on partition order-decreasing transformation semigroups ⋮ On the ranks of the semigroup of A-decreasing finite transformations ⋮ Representation theory of order-related monoids of partial functions as locally trivial category algebras ⋮ SPECTRUM CONVOLUTION OF FULL TRANSFORMATION SEMIGROUP ⋮ Unnamed Item ⋮ On certain infinite semigroups of order-decreasing transformations i ⋮ Abundance of $E$-order-preserving transformation semigroups ⋮ On certain semigroups of full contraction maps of a finite chain ⋮ ABUNDANCE OF THE SEMIGROUP OF ALL TRANSFORMATIONS OF A SET THAT REFLECT AN EQUIVALENCE RELATION ⋮ The Menger algebra of terms induced by order-decreasing transformations ⋮ NATURAL PARTIAL ORDER IN SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET ⋮ Unnamed Item ⋮ ISOMORPHISMS OF TRANSFORMATION SEMIGROUPS ASSOCIATED WITH SIMPLE DIGRAPHS ⋮ Abundant Semigroups of Transformations Preserving an Equivalence Relation ⋮ ℋ-Trivial Transformation Semibands and Digraphs ⋮ Abundance of Semigroups of Transformations Restricted by an Equivalence ⋮ Idempotent-generated semigroups and pseudovarieties ⋮ Presentations for subsemigroups of $PD_n$ ⋮ Transformation semigroups generated by semicomplete digraphs ⋮ Enumeration of certain finite semigroups of transformations ⋮ On nilpotent subsemigroups of the order-decreasing transformation semigroups

Cites Work

• Unnamed Item
• Unnamed Item
• Enumeration of injective partial transformations
• A market problem
• Idempotent rank in finite full transformation semigroups
• A combinatorial property of finite full transformation semigroups
• Abundant Semigroups
• Idempotent-connected abundant semigroups
• Idempotent generators in finite full transformation semigroups
• The Subsemigroup Generated By the Idempotents of a Full Transformation Semigroup
• Products of idempotents in certain semigroups of transformations

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