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
1. Verfasser: Plakhotnyk, Makar
Format: Artikel
Sprache:English
Veröffentlicht: 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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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-891
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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
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-03-21T07:47:49Z
collection 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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