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Algebra and Discrete Mathematics, 2013, Volume 16, Issue 1, Pages 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
Abstract:
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.
Keywords:
combinatorial inverse semigroup, group congruence, Möbius function, Möbius category.
Received: 20.05.2012 Revised: 30.07.2012
Citation:
E. D. Schwab, “Inverse semigroups generated by group congruences. The Möbius functions”, Algebra Discrete Math., 16:1 (2013), 116–126
Linking options:
https://www.mathnet.ru/eng/adm440 https://www.mathnet.ru/eng/adm/v16/i1/p116
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