On Jump-Critical Ordered Sets with Jump Number Four


Jump number
jump-critical ordered sets
tower poset.

How to Cite

E.M. Badr, & M.I. Moussa. (2014). On Jump-Critical Ordered Sets with Jump Number Four. Journal of Advances in Applied &Amp; Computational Mathematics, 1(1), 8–13. https://doi.org/10.15377/2409-5761.2014.01.01.2
Received 2014-10-24
Accepted 2014-10-24
Published 2014-10-10


For an ordered set P and for a linear extension L of P, let s(P,L) stand for the number of ordered pairs (x, y) of elements of P such that y is an immediate successor of x in L but y is not even above x in P. Put s(P) = min {s(P, L): Llinear extension of P}, the jump number of P. Call an ordered set P jump-critical if s(P - {x}) < s(P) for any ϵ P. We introduce some theorems about the jump-critical ordered sets with jump number four.



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