Combinatorial results for semigroups of orientation-preserving partial transformations

A. Umar

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let Xn = {1, 2,..., n}. On a partial transformation α: Dom α ⊆ Xn! Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is {pipe} Dom α {pipe}, the height of α is {pipe} Im α {pipe}, and the right (resp., left) waist of α is max(Im α) (resp., min(Im α)). We compute the cardinalities of some equivalences defined by equalities of these parameters on OPn, the semigroup of orientation-preserving full transformations of Xn, POPn the semigroup of orientation-preserving partial transformations of Xn, ORn the semigroup of orientation-preserving/reversing full transformations of Xn, and PORn the semigroup of orientation-preserving/reversing partial transformations of Xn, and their partial one-to-one analogue semigroups, POPIn and PORIn.

Original languageEnglish
JournalJournal of Integer Sequences
Volume14
Issue number7
Publication statusPublished - 2011

Fingerprint

Semigroup
Partial
Breadth
Min-max
Cardinality
Equality
Equivalence
Analogue

Keywords

  • Anti-cyclic sequence
  • Breadth
  • Cyclic sequence
  • Full transformation
  • Height
  • Left waist
  • Orientation-preserving transformation
  • Orientation-reversing transformation
  • Partial one-to-one transformation
  • Partial transformation
  • Right waist

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Combinatorial results for semigroups of orientation-preserving partial transformations. / Umar, A.

In: Journal of Integer Sequences, Vol. 14, No. 7, 2011.

Research output: Contribution to journalArticle

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