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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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/891 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | 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 \(\sigma\). |
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