On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs
Monfared, Keivan Hassani · Horn, Paul · Kenter, Franklin H. J. · Nowak, Kathleen · Sinkovic, John · Tobin, Josh
Original · EN
The principal permanent rank characteristic sequence is a binary sequence r₀ r₁ rₙ where rₖ = 1 if there exists a principal square submatrix of size k with nonzero permanent and rₖ = 0 otherwise, and r₀ = 1 if there is a zero diagonal entry. A characterization is provided for all principal permanent rank sequences obtainable by the family of nonnegative matrices as well as the family of nonnegative symmetric matrices. Constructions for all realizable sequences are provided. Results for skew-symmetric matrices are also included.
English translation
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