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Algebra and Discrete Mathematics, 2005, Issue 1, Pages 8–29 (Mi adm286)  

This article is cited in 4 scientific papers (total in 4 papers)

RESEARCH ARTICLE

Gorenstein matrices

M. A. Dokuchaeva, V. V. Kirichenkob, A. V. Zelenskyb, V. N. Zhuravlevb

a Departamento de Matematica Univ. de SãoPaulo, Caixa Postal 66281, São Paulo, SP, 05315–970 — Brazil
b Faculty of Mechanics and Mathematics, Kiev National, Taras Shevchenko Univ., Vladimirskaya Str., 64, 01033 Kiev, Ukraine
Full-text PDF (321 kB) Citations (4)
Abstract: 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 inxAn=2.
If a Latin square Ln with a first row and first column (0,1,,n1) 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 2m is a Latin square and a Gorenstein symmetric matrix with first row (0,1,,2m1) and
σ(Em)=(1232m12m2m2m12m221).
Keywords: exponent matrix; Gorenstein tiled order, Gorenstein matrix, admissible quiver, doubly stochastic matrix.
Received: 17.02.2005
Revised: 29.03.2005
Bibliographic databases:
Document Type: Article
MSC: 16P40, 16G10
Language: English
Citation: M. A. Dokuchaev, V. V. Kirichenko, A. V. Zelensky, V. N. Zhuravlev, “Gorenstein matrices”, Algebra Discrete Math., 2005, no. 1, 8–29
Citation in format AMSBIB
\Bibitem{DokKirZel05}
\by M.~A.~Dokuchaev, V.~V.~Kirichenko, A.~V.~Zelensky, V.~N.~Zhuravlev
\paper Gorenstein matrices
\jour Algebra Discrete Math.
\yr 2005
\issue 1
\pages 8--29
\mathnet{http://mi.mathnet.ru/adm286}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2148817}
\zmath{https://zbmath.org/?q=an:1091.16011}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Algebra and Discrete Mathematics
     
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