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Journal of Integer Sequences, Vol. 12 (2009), Article 09.4.8

Matrix Compositions


Emanuele Munarini
Politecnico di Milano
Dipartimento di Matematica
Piazza Leonardo da Vinci 32
20133 Milano
Italy

Maddalena Poneti and Simone Rinaldi
Università di Siena
Dipartimento di Scienze Matematiche e Informatiche
Pian dei Mantellini 44
53100 Siena
Italy

Abstract:

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.

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(Concerned with sequences A000670 A003242 A008275 A008277 A048933 A048994 A079500 A120733 A145839 A145840 A145841 and A161434.)

Received July 25 2008; revised version received June 16 2009. Published in Journal of Integer Sequences, June 20 2009.

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