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).Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|Keywords:||bijection, (2+2)-free poset, composition matrix, interval orders, dual poset, Electronic computers. Computer science, Computational Theory and Mathematics, Geometry and Topology, Theoretical Computer Science|
|Subjects:||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:||06 Jan 2017 10:10|