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Characterizing posets for which their natural transit functions coincide. (English) Zbl 1316.06003
Summary: The standard poset transit function of a poset \(P\) is a function \(T_P\) that assigns to a pair of comparable elements the interval between them, while \(T_P(x,y)=\{x,y\}\) for a pair \(x,y\) of incomparable elements. Posets in which the standard poset transit function coincides with the shortest-path transit function of its cover-incomparability graph are characterized in three ways, in particular with forbidden subposets.

MSC:
06A07 Combinatorics of partially ordered sets
05C38 Paths and cycles
05C12 Distance in graphs
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