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Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

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Composition matrices, (2+2)-free posets and their specializations

Dukes, Mark and Jelínek, Vit and Kubitzke, Martina (2011) Composition matrices, (2+2)-free posets and their specializations. The Electronic Journal of Combinatorics, 18 (1).

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Abstract

In this paper we present a bijection between composition matrices and (2 + 2)- free posets. This bijection maps partition matrices to factorial posets, and induces a bijection from upper triangular matrices with non-negative entries having no rows or columns of zeros to unlabeled (2 + 2)-free posets. Chains in a (2 + 2)-free poset are shown to correspond to entries in the associated composition matrix whose hooks satisfy a simple condition. It is shown that the action of taking the dual of a poset corresponds to reflecting the associated composition matrix in its anti-diagonal. We further characterize posets which are both (2 + 2)- and (3 + 1)-free by certain properties of their associated composition matrices.