Some combinatorial problems in the theory of partial transformation semigroups

• Datum: 2014
• 1. Verfasser: Umar, A.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2014
• Schriftenreihe: Algebra and Discrete Mathematics
• Online Zugang: http://dspace.nbuv.gov.ua/handle/123456789/152350
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Some combinatorial problems in the theory of partial transformation semigroups / A. Umar // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 1. — С. 110–134. — Бібліогр.: 56 назв. — англ.

Let Xn = {1,2,…,n}. On a partial transformation α : Dom α ⊆ Xn → Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is ∣ Dom α ∣, the collapse of α is c(α) = ∣ ∪t∈Imα{tα⁻¹ :∣ tα⁻¹ ∣≥ 2} ∣, fix of α is f(α) = ∣ {x ∈ Xn : xα = x} ∣, the height of α is ∣ Imα ∣, and the rig...