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2006

A Counting of the minimal realizations of the posets of dimension two

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A Counting of the minimal realizations of the posets of dimension two
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. Mathematics Subject Classi cations (1991): Key words: Counting Dimension Directed Graphs Gallai's Partition Indecomposable Posets Realization.
Pierre Ille, Jean-Xavier Rampon
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2006
Where ARSCOM
Authors Pierre Ille, Jean-Xavier Rampon
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