Inverse semigroups generated by group congruences. The Möbius functions
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 poset...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2013 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152314 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Inverse semigroups generated by group congruences. The Möbius functions / E.D. Schwab // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 1. — С. 116–126. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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.
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| ISSN: | 1726-3255 |