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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2013, Volume 16, Issue 1, Pages 116–126 (Mi adm440)

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.

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Bibliographic databases:
MSC: 20M18, 06A07
Revised: 30.07.2012
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Citation: E. D. Schwab, “Inverse semigroups generated by group congruences. The Möbius functions”, Algebra Discrete Math., 16:1 (2013), 116–126

Citation in format AMSBIB
\Bibitem{Sch13} \by E.~D.~Schwab \paper Inverse semigroups generated by group congruences. The M\"{o}bius functions \jour Algebra Discrete Math. \yr 2013 \vol 16 \issue 1 \pages 116--126 \mathnet{http://mi.mathnet.ru/adm440} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184704}