On Jump-Critical Ordered Sets with Jump Number Four
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Keywords

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

Abstract

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.

https://doi.org/10.15377/2409-5761.2014.01.01.2
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References

Dilworth RP. A decomposition theorem for partially ordered sets. Ann Math 1950; 51: 161-166. http://dx.doi.org/10.2307/1969503

El-Zahar MH, Rival I. Examples of jump - critical ordered sets. SIAM J Algebraic Discrete Methods 1985; 6(4): 713- 720. http://dx.doi.org/10.1137/0606069

El-Zahar MH, Schemer JH. On the size of jump-critical ordered sets. Order 1984; 1: 3-5.

Hell P, Li W, Schmerl JH. Jump number and width. Order 1986; 5: 227-234.

Habib M. Comparability invariants, in Ordres: description et roles (eds. M. Pouzet and D. Richard), North Holland, Amsterdam 1984; 371-386.

El-Zahar MH. On Jump-Critical Posets with Jump-Number Equal to Width. Order 2000; 17: 93-101.

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Copyright (c) 2014 E.M. Badr, M.I. Moussa