Convex (0,1)-matrices and their epitopes

Convex (0,1)-matrices and their epitopes

We investigate (0,1)-matrices that are convex, which means that the ones are consecutive in every row and column. These matrices occur in discrete tomography. The notion of ranked essential sets, known for permutation matrices, is extended to convex sets. We show a number of results for the class C(...

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Veröffentlicht in:Discrete Applied Mathematics 2021-07, Vol.297, p.21-34
Hauptverfasser: Brualdi, Richard A., Dahl, Geir
Format: Artikel
Sprache:eng
Schlagworte:
Convexity
Essential set
Mathematical analysis
Matrix methods
Permutation matrix
Permutations
Polyomino
Zero-one matrix
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Zusammenfassung:We investigate (0,1)-matrices that are convex, which means that the ones are consecutive in every row and column. These matrices occur in discrete tomography. The notion of ranked essential sets, known for permutation matrices, is extended to convex sets. We show a number of results for the class C(R,S) of convex matrices with given row and column sum vectors R and S. Also, it is shown that the ranked essential set uniquely determines a matrix in C(R,S).
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2021.02.038