Geodesic
Additive decomposition of matrices under rank conditions and zero pattern constraints
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 825-854.

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This paper deals with additive decompositions $A=A_1+\cdots +A_p$ of a given matrix $A$, where the ranks of the summands $A_1,\ldots , A_p$ are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs.
DOI : 10.21136/CMJ.2022.0185-21
Classification : 05C20, 05C50, 15A03, 15A21
Keywords: additive decomposition; rank constraint; zero pattern constraint; directed bipartite graph; $ß{L}$-free directed bipartite graph; permutation $ß{L}$-free directed bipartite graph; Bell number; Stirling partition number 
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     title = {Additive decomposition of matrices under rank conditions and zero pattern constraints},
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Bart, Harm; Ehrhardt, Torsten. Additive decomposition of matrices under rank conditions and zero pattern constraints. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 825-854. doi : 10.21136/CMJ.2022.0185-21. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0185-21/

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