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{\bf Mark Dukes, V\'it Jel\'inek and Martina Kubitzke}
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{\bf Composition Matrices, (2+2)-Free Posets and their Specializations}
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In this paper we present a bijection between composition matrices and
($\mathbf{2+2}$)-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 ($\mathbf{2+2}$)-free posets.  Chains in a
($\mathbf{2+2}$)-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 ($\mathbf{2+2}$)- and
($\mathbf{3+1}$)-free by certain properties of their associated
composition matrices.

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