Maximum Rank of Powers of a Matrix of a Given Pattern

DOI10.2307/2047304zbMath0695.05043OpenAlexW4254969455MaRDI QIDQ3470496

Svatopluk Poljak

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2047304

zbMATH Keywords

digraphmaximum rankmaximum number of independent p-walkspattern of a matrix

Mathematics Subject Classification ID

Paths and cycles (05C38) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Directed graphs (digraphs), tournaments (05C20)

Related Items (12)

Some combinatorial-algebraic problems from complexity theory ⋮ Algebraic techniques in communication complexity ⋮ Computing the generic jordan canonical form ⋮ Asymptotics of the Jordan normal form of a random nilpotent matrix ⋮ Generic properties and control of linear structured systems: A survey ⋮ Commuting nilpotent matrices and Artinian algebras. ⋮ Bound on the Jordan type of a generic nilpotent matrix commuting with a given matrix ⋮ Nilpotent matrices having a given Jordan type as maximum commuting nilpotent orbit ⋮ The generic canonical form of a regular structured matrix pencil ⋮ Finite posets and Ferrers shapes ⋮ On the rank and periodic rank of finite dynamical systems ⋮ Some recent results in combinatorial approaches to dynamical systems

Cites Work

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• A combinatorial approach to matrix algebra
• The Role of Unimodularity in Applying Linear Inequalities to Combinatorial Theorems
• Systems of distinct representatives and linear algebra
• An $n^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs

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