A lower bound on the maximum permanent in \(\Lambda_{n}^{k}\).

DOI10.1016/S0024-3795(02)00715-2zbMath1048.15010MaRDI QIDQ1414135

Ian M. Wanless

Publication date: 19 November 2003

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

permanentLatin rectangle\((0,1)\) matrixregular bipartite graphBregman boundMerriell's conjectures

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Determinants, permanents, traces, other special matrix functions (15A15) Matrices of integers (15B36)

Related Items (7)

Lower Bounds for Partial Matchings in Regular Bipartite Graphs and Applications to the Monomer–Dimer Entropy ⋮ A relationship between subpermanents and the arithmetic-geometric mean inequality ⋮ An update on Minc's survey of open problems involving permanents ⋮ Counting Matchings and Tree-Like Walks in Regular Graphs ⋮ Matchings and independent sets of a fixed size in regular graphs ⋮ Theory of computation of multidimensional entropy with an application to the monomer-dimer problem ⋮ On Minc's sixth Conjecture

Cites Work

• A vector space analog of permutations with restricted position
• Hermite polynomials and a duality relation for matchings polynomials
• Maximising the permanent and complementary permanent of (0,1)-matrices with constant line sum
• Maximising the permanent of \((0,1)\)-matrices and the number of extensions of Latin rectangles
• Counting 1-factors in regular bipartite graphs
• Theory of monomer-dimer systems
• The maximum permanent in
• Asymptotic enumeration of Latin rectangles
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