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Some combinatorial problems in the theory of symmetric inverse semigroups
Репозиторій DSpace/Manakin
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Some combinatorial problems in the theory of symmetric inverse semigroups
Інший ID:
2000 Mathematics Subject Classification:20M18, 20M20, 05A10, 05A15
Посилання:
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.
Підтримка:
The ideas for this work were formed during a one month stay at Wilfrid LaurierUniversity in the Summer of 2007.2This paper is based on the talk I gave at the 22nd BCC Conference, University ofSt Andrews, July 2009.
Дата:
2010
Переглядів:
354
Завантажень:
316
Анотація:
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)=|{x∈Xn:xα=x}|. The cardinalities of some equivalences defined by equalities of these parameters on In, the semigroup of partial one-one mappings of Xn, and some of its notable subsemigroups that have been computed are gathered together and the open problems highlighted.
