Composition matrices, \((2+2)\)-free posets and their specializations
Summary: 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.
scientific article; zbMATH DE number 5902974