RESEARCH ARTICLE

Almost all derivative quivers of artinian biserial rings contain chains

Tetjana Avdeeva^a, Olexandr Ganyushkin<sup>b

a</sup> National Technical University of Ukraine "Kiev Polytechnic Institute", Kyiv, Ukraine Department of Physics and Mathematics, National of Technical University of Ukraine "Kyiv of Polytechnical Institute", 37, Peremohy pr., Kyiv, UKRAINE
^b Department ofMechanics and Mathematics, Kyiv Taras Shevchenko University, 64, Volodymyrska st., 01033, Kyiv, UKRAINE

Abstract: A lower estimate for the number $M_n$ of all labelled quivers with $n$–vertex parts of Artinian biserial rings is given and the asymptotic of the relation $M_n /B_n$, where $B_n$ denotes the number of those quivers all connected components of which are cycles, is studied.

Keywords: artinian rings, quivers, bipartite graphs.

MSC: 05C30, 05C38, 16P20

Received: 06.12.2002

Language: English

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