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). P44. (http://www.combinatorics.org/Volume_18/PDF/v18i1p4...)
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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.
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Item type: Article ID code: 34523 Dates: DateEvent2011PublishedSubjects: Science > Mathematics > Electronic computers. Computer science Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 18 Oct 2011 11:49 Last modified: 08 Apr 2024 19:32 URI: https://strathprints.strath.ac.uk/id/eprint/34523