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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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/761 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543216212377600 |
|---|---|
| author | Schwab, Emil Daniel |
| author_facet | Schwab, Emil Daniel |
| author_sort | Schwab, Emil Daniel |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T01:26:05Z |
| 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. |
| first_indexed | 2025-12-02T15:40:55Z |
| format | Article |
| id | admjournalluguniveduua-article-761 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:40:55Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-7612018-04-26T01:26:05Z Inverse semigroups generated by group congruences. The Möbius functions Schwab, Emil Daniel combinatorial inverse semigroup, group congruence, Möbius function, Möbius category 20M18, 06A07 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. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/761 Algebra and Discrete Mathematics; Vol 16, No 1 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/761/290 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | combinatorial inverse semigroup group congruence Möbius function Möbius category 20M18 06A07 Schwab, Emil Daniel Inverse semigroups generated by group congruences. The Möbius functions |
| title | 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_short | Inverse semigroups generated by group congruences. The Möbius functions |
| title_sort | inverse semigroups generated by group congruences. the möbius functions |
| topic | combinatorial inverse semigroup group congruence Möbius function Möbius category 20M18 06A07 |
| topic_facet | combinatorial inverse semigroup group congruence Möbius function Möbius category 20M18 06A07 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/761 |
| work_keys_str_mv | AT schwabemildaniel inversesemigroupsgeneratedbygroupcongruencesthemobiusfunctions |