The ranks of certain semigroups of partial isometries

Bugay L., YAĞCI M., AYIK H.

SEMIGROUP FORUM, vol.97, no.2, pp.214-222, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 97 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1007/s00233-018-9954-1
  • Journal Name: SEMIGROUP FORUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.214-222
  • Çukurova University Affiliated: Yes

Abstract

Let In be the symmetric inverse semigroup on X-n = {1,..., n}, and let DPn and ODPn be its subsemigroups of partial isometries and of order-preserving partial isometries on Xn under its natural order, respectively. In this paper we find the ranks of the subsemigroups DPn, r = {alpha is an element of DPn : | im (alpha)vertical bar = r} and ODPn, r = {a. ODPn : vertical bar im (a)vertical bar <= r} for 2 <= r <= n - 1.