ON JUMP- CRITICAL ORDERED SETS | ||||
| The International Conference on Mathematics and Engineering Physics | ||||
| Article 2, Volume 5, International Conference on Mathematics and Engineering Physics (ICMEP-5), May 2010, Page 1-8 PDF (208.08 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/icmep.2010.29770 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
| E. M. Badr1; M. I. Moussa2 | ||||
| 1Mathematics and computer Science Department, Faculty of Science, Benha University, Benha, Egypt. | ||||
| 2Faculty of computer & information Benha University, Benha, Egypt. | ||||
| Abstract | ||||
| 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) : L linear extension of P}, the jump number of P. Call an ordered set P is jump-critical if s (P-{x}) < s (P) for any xP. We introduce some theory about the jump-critical ordered sets with jump number four. Especially, we introduce a complete list of the jump-critical ordered sets with jump number four ( it has four maximal elements). Finally, we prove that a k-critical ordered set is a k-tower ( its width is 2, k >1). KEYWORDS: Jump number, jump-critical ordered sets. | ||||
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