Geodesic
Matrix compositions
Journal of integer sequences, Tome 12 (2009) no. 4
In this paper we study the class of $m$-row matrix compositions ($m$-com positions, for short), i.e., $m$-row matrices with nonnegative integer entries in which every column has at least one non-zero element. We provide several enumerative results, various combinatorial identities, and some combinatorial interpretations. Most of these properties are an extension to matrix compositions of the combinatorial properties of ordinary compositions.
Classification : 05A17, 05A15
Keywords: compositions, multisets, Cassini identity, carlitz compositions, palindromic compositions, preferential arrangements, bargraphs, Stirling number, enumeration 
@article{JIS_2009__12_4_a5,
     author = {Munarini,  Emanuele and Poneti,  Maddalena and Rinaldi,  Simone},
     title = {Matrix compositions},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {4},
     zbl = {1213.05017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_4_a5/}
}
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Munarini,  Emanuele; Poneti,  Maddalena; Rinaldi,  Simone. Matrix compositions. Journal of integer sequences, Tome 12 (2009) no. 4. http://geodesic.mathdoc.fr/item/JIS_2009__12_4_a5/