A generalization of the all minors matrix tree theorem to semirings

DOI10.1016/S0012-365X(98)00204-0zbMath0928.15010OpenAlexW2060388682MaRDI QIDQ1297437

Michel Minoux

Publication date: 9 January 2000

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0012-365x(98)00204-0

zbMATH Keywords

treeweighted graphdeterminantminorssemiringsforestbideterminant

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items

Dioïds and semirings: Links to fuzzy sets and other applications, On simultaneously nilpotent antiring matrices, On invertible matrices over antirings, Invertible matrices and semilinear spaces over commutative semirings, On nilpotent matrices over antirings, Derivations of matrix semirings, On generalized fuzzy matrices with periods, On nilpotency of matrices over antirings, On nilpotency of generalized fuzzy matrices, Extension of MacMahon's master theorem to pre-semi-rings, Forest matrices around the Laplacian matrix

Cites Work

• Line-digraphs, arborescences and theorems of Tutte and Knuth
• A Combinatorial Proof of the All Minors Matrix Tree Theorem
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