Some combinatorial problems in the theory of symmetric inverse semigroups

• Published in: Algebra and Discrete Mathematics
• Date: 2010
• Main Author: Umar, A.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/154602
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Some combinatorial problems in the theory of symmetric inverse semigroups / A. Umar // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 113–124. — Бібліогр.: 32 назв. — англ.

Let Xn={1,2,⋯,n} and let α:Domα⊆Xn→Imα⊆Xn be a (partial) transformation on Xn. On a partial one-one mapping of Xn the following parameters are defined: the height of α is h(α)=|Imα|, the right [left] waist of α is w+(α)=max(Imα)[w−(α)=min(Imα)], and fix of α is denoted by f(α), and defined by f(α)...