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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| Datum: | 2018 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/891 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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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 |
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Algebra and Discrete Mathematics |
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|
| datestamp_date |
2018-03-21T07:47:49Z |
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OJS |
| language |
English |
| topic |
Gorenstein matrix Gorenstein tiled order |
| spellingShingle |
Gorenstein matrix Gorenstein tiled order Plakhotnyk, Makar On the dimension of Kirichenko space |
| topic_facet |
Gorenstein matrix Gorenstein tiled order |
| format |
Article |
| author |
Plakhotnyk, Makar |
| author_facet |
Plakhotnyk, Makar |
| author_sort |
Plakhotnyk, Makar |
| title |
On the dimension of Kirichenko space |
| title_short |
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_sort |
on the dimension of kirichenko space |
| 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 \(\sigma\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/891 |
| work_keys_str_mv |
AT plakhotnykmakar onthedimensionofkirichenkospace |
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2025-12-02T15:33:10Z |
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2025-12-02T15:33:10Z |
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1850412105640968192 |