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On the Height and Jump Number of Ordered Sets
Ahmad Sharary, Nejib Zaguia and Mohammad Alzohairi

Let P be a finite ordered set. One can easily show that w(P)−1 ≤ s(P) ≤ |P|−h(P), where s(P) is the jump number of P, w(P) is the width of P and h(P) is the height of P. The recognition problem of ordered sets for which w(P) − 1 = s(P) “called Dilworth posets” is NP-complete. The purpose of this paper is to give an “effective” characterization of all ordered sets P for which s(P)=|P|−h(P).

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