On monoids of monotone partial transformations of a finite chain whose domainand ranges are intervals

AYIK H., Fernandand V. H., KORKMAZ E.

Algebra and Discrete Mathematics, cilt.40, sa.1, 2025 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.12958/adm2403
  • Dergi Adı: Algebra and Discrete Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: monotone, presentations, rank, transformations
  • Çukurova Üniversitesi Adresli: Evet

Özet

In this note, we consider the monoid PIMn of all partial monotone transformations on a chain with n elements whose domains and ranges are intervals and its submonoid IMn constituted by the full transformations. For both of these monoids, our aim is to determine their cardinalities and ranks and define them by means of presentations. We also calculate the number of nilpotent elements of PIMn .