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)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.
| Item type: | Article |
|---|---|
| ID code: | 34523 |
| Keywords: | bijection, (2+2)-free poset, composition matrix, interval orders, dual poset, Electronic computers. Computer science |
| Subjects: | Science > Mathematics > Electronic computers. Computer science |
| Department: | Faculty of Science > Computer and Information Sciences |
| Related URLs: | |
| Depositing user: | Pure Administrator |
| Date Deposited: | 18 Oct 2011 12:49 |
| Last modified: | 12 Jul 2012 11:56 |
| URI: | http://strathprints.strath.ac.uk/id/eprint/34523 |
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