On the dimension of Kirichenko space
We introduce a notion of the Kirichenko space which is connected with the notion of Gorenstein matrix (see [2], ch. 14). Every element of Kirichenko space is an \(n\times n\) matrix, whose elements are solutions of the equations \(a_{i,j}+a_{j,\sigma (i)} =a_{i,\sigma (i)}\); \(a_{1,i}=0\) for \(i,...
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/891 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543276450971648 |
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| author | Plakhotnyk, Makar |
| author_facet | Plakhotnyk, Makar |
| author_sort | Plakhotnyk, Makar |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T07:47:49Z |
| description | We introduce a notion of the Kirichenko space which is connected with the notion of Gorenstein matrix (see [2], ch. 14). Every element of Kirichenko space is an \(n\times n\) matrix, whose elements are solutions of the equations \(a_{i,j}+a_{j,\sigma (i)} =a_{i,\sigma (i)}\); \(a_{1,i}=0\) for \(i,j =1,\ldots, n\) determined by a permutation \(\sigma\) which has no cycles of the length \(1\). We give a formula for the dimension of this space in terms of the cyclic type of \(\sigma\). |
| first_indexed | 2025-12-02T15:33:10Z |
| format | Article |
| id | admjournalluguniveduua-article-891 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:33:10Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-8912018-03-21T07:47:49Z On the dimension of Kirichenko space Plakhotnyk, Makar Gorenstein matrix, Gorenstein tiled order We introduce a notion of the Kirichenko space which is connected with the notion of Gorenstein matrix (see [2], ch. 14). Every element of Kirichenko space is an \(n\times n\) matrix, whose elements are solutions of the equations \(a_{i,j}+a_{j,\sigma (i)} =a_{i,\sigma (i)}\); \(a_{1,i}=0\) for \(i,j =1,\ldots, n\) determined by a permutation \(\sigma\) which has no cycles of the length \(1\). We give a formula for the dimension of this space in terms of the cyclic type of \(\sigma\). Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/891 Algebra and Discrete Mathematics; Vol 5, No 2 (2006) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/891/420 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Gorenstein matrix Gorenstein tiled order Plakhotnyk, Makar On the dimension of Kirichenko space |
| title | On the dimension of Kirichenko space |
| title_full | On the dimension of Kirichenko space |
| title_fullStr | On the dimension of Kirichenko space |
| title_full_unstemmed | On the dimension of Kirichenko space |
| title_short | On the dimension of Kirichenko space |
| title_sort | on the dimension of kirichenko space |
| topic | Gorenstein matrix Gorenstein tiled order |
| topic_facet | Gorenstein matrix Gorenstein tiled order |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/891 |
| work_keys_str_mv | AT plakhotnykmakar onthedimensionofkirichenkospace |