On the semigroups of fence-decreasing and fence-preserving transformations on a finite fence

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AYIK G., AYIK H., Dimitrova I., Koppitz J.

Mathematica Slovaca, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1515/ms-2026-0373
  • Dergi Adı: Mathematica Slovaca
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
  • Anahtar Kelimeler: fence-decreasing, fence-preserving, generating set, rank, transformation semigroups, zig–zig order
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Çukurova Üniversitesi Adresli: Evet

Özet

For a natural number n, a fence [n] = {1 ≺ 2 ≻ 3 ≺ 4 ≻ 5 ≺⋯n} is a partial ordered set. A partial transformation α is called fence-decreasing if xα ⪯ x for all x in the domain of α, and fence-preserving if x ≺ y implies xα ⪯ yα for all x and y in the domain of α. In this paper, we consider the monoids DFn (PDFn) of all fence-decreasing full (partial) transformations as well as the monoid PCFn of all fence-preserving transformations of PDFn. For these three monoids and some of their ideals, we determine the unique minimal generating set. Moreover, we calculate the rank of DFn, PDFn, and PCFn. Additional, we provide several combinatorial results concerning these three monoids.