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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1996, Volume 59, Issue 5, Pages 643–662 (Mi mz1759)

Partially decomposable and totally indecomposable nonnegative matrices

Yu. V. Bolotnikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider $m\times n$, $m\le n$, matrices with entries from an arbitrary given finite set of nonnegative real numbers, including zero. In particular, $(0,1)$-matrices are studied. On the basis of the classification of such matrices by type and of the general formula for the number of matrices of nullity $t$ valid for $t>n$ and $t\ge n>m$ (see [2]), an asymptotic (as $n\to\infty$) expansion is obtained for the total number of: (a) totally indecomposable matrices (Theorems 1 and 5), (b) partially decomposable matrices of given nullity $t\ge n$ (Theorems 2 and 4), (c) matrices with zero permanent (without using the inclusion-exclusion principle; Corollary of Theorem 2).

DOI: https://doi.org/10.4213/mzm1759

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English version:
Mathematical Notes, 1996, 59:5, 463–476

Bibliographic databases:

UDC: 517

Citation: Yu. V. Bolotnikov, “Partially decomposable and totally indecomposable nonnegative matrices”, Mat. Zametki, 59:5 (1996), 643–662; Math. Notes, 59:5 (1996), 463–476

Citation in format AMSBIB
\Bibitem{Bol96} \by Yu.~V.~Bolotnikov \paper Partially decomposable and totally indecomposable nonnegative matrices \jour Mat. Zametki \yr 1996 \vol 59 \issue 5 \pages 643--662 \mathnet{http://mi.mathnet.ru/mz1759} \crossref{https://doi.org/10.4213/mzm1759} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1445446} \zmath{https://zbmath.org/?q=an:0877.15024} \transl \jour Math. Notes \yr 1996 \vol 59 \issue 5 \pages 463--476 \crossref{https://doi.org/10.1007/BF02308812} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996VM73200001}