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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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2013 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/152314 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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| id |
nasplib_isofts_kiev_ua-123456789-152314 |
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Schwab, E.D. 2019-06-09T17:23:16Z 2019-06-09T17:23:16Z 2013 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. 1726-3255 2010 MSC:20M18, 06A07. https://nasplib.isofts.kiev.ua/handle/123456789/152314 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Inverse semigroups generated by group congruences. The Möbius functions Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Inverse semigroups generated by group congruences. The Möbius functions |
| spellingShingle |
Inverse semigroups generated by group congruences. The Möbius functions Schwab, E.D. |
| title_short |
Inverse semigroups generated by group congruences. The Möbius functions |
| title_full |
Inverse semigroups generated by group congruences. The Möbius functions |
| title_fullStr |
Inverse semigroups generated by group congruences. The Möbius functions |
| title_full_unstemmed |
Inverse semigroups generated by group congruences. The Möbius functions |
| title_sort |
inverse semigroups generated by group congruences. the möbius functions |
| author |
Schwab, E.D. |
| author_facet |
Schwab, E.D. |
| publishDate |
2013 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/152314 |
| citation_txt |
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. |
| work_keys_str_mv |
AT schwabed inversesemigroupsgeneratedbygroupcongruencesthemobiusfunctions |
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2025-12-07T15:45:50Z |
| last_indexed |
2025-12-07T15:45:50Z |
| _version_ |
1850864934127140864 |