Gorenstein matrices
Let A = (aij ) be an integral matrix. We say that
 A is (0, 1, 2)-matrix if aij ∈ {0, 1, 2}. There exists the Gorenstein
 (0, 1, 2)-matrix for any permutation σ on the set {1, . . . , n} without fixed elements. For every positive integer n there exists the
 Gorenstein cyclic...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2005 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/156609 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Gorenstein matrices / M.A. Dokuchaev, V.V. Kirichenko, A.V. Zelensky, V.N. Zhuravlev // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 8–29. — Бібліогр.: 24 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862708677675319296 |
|---|---|
| author | Dokuchaev, M.A. Kirichenko, V.V. Zelensky, A.V. Zhuravlev, V.N. |
| author_facet | Dokuchaev, M.A. Kirichenko, V.V. Zelensky, A.V. Zhuravlev, V.N. |
| citation_txt | Gorenstein matrices / M.A. Dokuchaev, V.V. Kirichenko, A.V. Zelensky, V.N. Zhuravlev // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 8–29. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let A = (aij ) be an integral matrix. We say that
A is (0, 1, 2)-matrix if aij ∈ {0, 1, 2}. There exists the Gorenstein
(0, 1, 2)-matrix for any permutation σ on the set {1, . . . , n} without fixed elements. For every positive integer n there exists the
Gorenstein cyclic (0, 1, 2)-matrix An such that inx An = 2.
If a Latin square Ln with a first row and first column (0, 1, . . .
n − 1) is an exponent matrix, then n = 2m and Ln is the Cayley
table of a direct product of m copies of the cyclic group of order 2.
Conversely, the Cayley table Em of the elementary abelian group
Gm = (2)×. . .×(2) of order 2
m is a Latin square and a Gorenstein
symmetric matrix with first row (0, 1, . . . , 2
m − 1) and
σ(Em) = 
1 2 3 . . . 2
m − 1 2m
2
m 2
m − 1 2m − 2 . . . 2 1 .
|
| first_indexed | 2025-12-07T17:12:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156609 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:12:55Z |
| publishDate | 2005 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Dokuchaev, M.A. Kirichenko, V.V. Zelensky, A.V. Zhuravlev, V.N. 2019-06-18T17:50:15Z 2019-06-18T17:50:15Z 2005 Gorenstein matrices / M.A. Dokuchaev, V.V. Kirichenko, A.V. Zelensky, V.N. Zhuravlev // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 8–29. — Бібліогр.: 24 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 16P40; 16G10. https://nasplib.isofts.kiev.ua/handle/123456789/156609 Let A = (aij ) be an integral matrix. We say that
 A is (0, 1, 2)-matrix if aij ∈ {0, 1, 2}. There exists the Gorenstein
 (0, 1, 2)-matrix for any permutation σ on the set {1, . . . , n} without fixed elements. For every positive integer n there exists the
 Gorenstein cyclic (0, 1, 2)-matrix An such that inx An = 2.
 If a Latin square Ln with a first row and first column (0, 1, . . .
 n − 1) is an exponent matrix, then n = 2m and Ln is the Cayley
 table of a direct product of m copies of the cyclic group of order 2.
 Conversely, the Cayley table Em of the elementary abelian group
 Gm = (2)×. . .×(2) of order 2
 m is a Latin square and a Gorenstein
 symmetric matrix with first row (0, 1, . . . , 2
 m − 1) and
 σ(Em) = 
 1 2 3 . . . 2
 m − 1 2m
 2
 m 2
 m − 1 2m − 2 . . . 2 1 . The first author was partially supported by CNPq of Brazil, Proc.
 304658/2003-0.
 The second author thanks the Institute of Mathenatics and Statistics
 of the University of S˜ao Paulo for the hospitality during his visit, which
 was supported by FAPESP of Brazil, Proc. 02/05087-2. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Gorenstein matrices Article published earlier |
| spellingShingle | Gorenstein matrices Dokuchaev, M.A. Kirichenko, V.V. Zelensky, A.V. Zhuravlev, V.N. |
| title | Gorenstein matrices |
| title_full | Gorenstein matrices |
| title_fullStr | Gorenstein matrices |
| title_full_unstemmed | Gorenstein matrices |
| title_short | Gorenstein matrices |
| title_sort | gorenstein matrices |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156609 |
| work_keys_str_mv | AT dokuchaevma gorensteinmatrices AT kirichenkovv gorensteinmatrices AT zelenskyav gorensteinmatrices AT zhuravlevvn gorensteinmatrices |