Generating sets of certain finite subsemigroups of monotone partial bijections


Bugay L. , AYIK H.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, ss.2270-2278, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 42 Konu: 5
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1710-86
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayısı: ss.2270-2278

Özet

Let I-n, be the symmetric inverse semigroup, and let PODIn and POIn be its subsemigroups of monotone partial bijections and of isotone partial bijections on X-n = {1, . . . , n} under its natural order, respectively. In this paper we characterize the structure of (minimal) generating sets of the subsemigroups PODIn,r = {alpha is an element of PODIn :vertical bar im (alpha) vertical bar <= r} , POIn,r {alpha is an element of POIn : vertical bar im (alpha) vertical bar <= r} , and E-n,E-r = {id (A) is an element of I-n : A subset of X-n and vertical bar A vertical bar <= r} where id(A) is the identity map on A subset of X-n for 0 <= r <= n - 1.