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Algebra and Discrete Mathematics, 2013, том 16, выпуск 1, страницы 116–126
(Mi adm440)
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RESEARCH ARTICLE
Inverse semigroups generated by group congruences. The Möbius functions
E. D. Schwab Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, Texas 79968
Аннотация:
The computation of the Möbius function of a Möbius category that arises from a combinatorial inverse semigroup has a distinctive feature. This computation is done on the field of finite posets. In the case of two combinatorial inverse semigroups, order isomorphisms between corresponding finite posets reduce the computation to one of the semigroups. Starting with a combinatorial inverse monoid and using a group congruence we construct a combinatorial inverse semigroup such that the Möbius function becomes an invariant to this construction. For illustration, we consider the multiplicative analogue of the bicyclic semigroup and the free monogenic inverse monoid.
Ключевые слова:
combinatorial inverse semigroup, group congruence, Möbius function, Möbius category.
Поступила в редакцию: 20.05.2012 Исправленный вариант: 30.07.2012
Образец цитирования:
E. D. Schwab, “Inverse semigroups generated by group congruences. The Möbius functions”, Algebra Discrete Math., 16:1 (2013), 116–126
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm440 https://www.mathnet.ru/rus/adm/v16/i1/p116
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