The posets of dimension \(2\) are those posets whose minimal realizations have two elements, that is, which may be obtained as the intersection of two of their linear extensions. Gallai’s decomposition of a poset allows for a simple formula to count the number of the distinct minimal realizations of the posets of dimension \(2\). As an easy consequence, the characterization of M. El-Zahar and of N.W. Sauer of the posets of dimension \(2\), with an unique minimal realization, is obtained.
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