A general approach for generating sets of certain subsemigroups of monotone maps


BUGAY L.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.13, no.7, 2020 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 7
  • Publication Date: 2020
  • Doi Number: 10.1142/s1793557120501326
  • Title of Journal : ASIAN-EUROPEAN JOURNAL OF MATHEMATICS

Abstract

Let T-n and P-n be the monoids of all (full) transformations and of all partial transformations, on a finite chain X-n = {1,..., n} under its natural order, respectively. Moreover, let ODn,r (PODn,r) be the subsemigroup of T-n (P-n) consists of all monotone transformations (monotone partial transformations) with height less than or equal to r for 1 <= r <= n-1 (0 <= r <= n-1). In this paper, we develop a new and general approach to find a (minimal) generating set of ODn,r (PODn,r).