Combinatorial results for semigroups of order-preserving or order-reversing subpermutations

A. Laradji, A. Umar

Research output: Contribution to journalArticle

Abstract

Let (Formula presented.) For a partial one–one transformation (or subpermutation) (Formula presented.) of (Formula presented.) the following parameters are defined: the height (Formula presented.) , the waist (Formula presented.) , and the fix (Formula presented.). We compute the cardinalities of some equivalence classes defined by equalities of these parameters on (Formula presented.) and (Formula presented.) the semigroups of order-preserving and of order-preserving or order-reversing subpermutations of (Formula presented.) respectively. As a consequence, we obtain several formulae and generating functions for the number of nilpotents in (Formula presented.) and (Formula presented.). We also prove that, for large (Formula presented.) a randomly chosen order-preserving (resp. order-reversing) subpermutation of (Formula presented.) has probability (Formula presented.) (resp. (Formula presented.) ) of being nilpotent.

Original languageEnglish
Pages (from-to)269-283
Number of pages15
JournalJournal of Difference Equations and Applications
Volume21
Issue number3
DOIs
Publication statusPublished - Mar 4 2015

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Keywords

  • asymptotic behaviour
  • generating function
  • nilpotent transformation
  • order-preserving and order-reversing subpermutations
  • recurrence relation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Analysis

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