# ON THE JUMP NUMBER OF SPLITS OF ORDERED SETS

• Jung, Hyung-Chan (Liberal Arts and Sciences, Korea University of Technology and Education) ;
• Lee, Jeh-Gwon (Department of Mathematics, Sogang University)
• Published : 2000.11.01

#### Abstract

In this paper, we consider the jump number of the split P[S] of a subset S ordered set P. $For\ x\in\ P,\ we\ show\ that\ s(P)\leq\ s(P[x]\leq\ s(P)+2$ and give a necessary and sufficient condition for which s(P[x])=s(P).

#### References

1. Ann. Disc. Math. v.9 The jump number of dags and posets: an introduction M. Chein;H. Habib
2. Ars Combinatoria v.40 On the product of some posets: jump number and greediness H. C. Jung
3. On the jump number of lexiographic sums of ordered sets H. C. Jung;J. G. Lee
4. Extremal problems in dimension theory for ordered setsl R. Kimble
5. Fund. Math. v.16 Sur l'extension de l'ordre partiel E. Szpilrajn