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, Volume 17, Issue 1, pp 93–101 | Cite as

On Jump-Critical Posets with Jump-Number Equal to Width

  • Mohamed H. El-Zahar
Article
  • 29 Downloads

Abstract

We investigate the structure of m-jump-critical posets P with w(P) = m. We prove that the size of such posets satisfies |P| ≤ 3m2. For the special when the maximum antichain occurs as the maximal (or minimal) elements, we have the sharp upper bound |P| ≤ 3m - k; where k = min {|{Max}(P)|, |{Min}(P)|}. We give examples of posets which illustrate the explored structure of these m-jump-critical posets P with width m.

jump-number jump-critical posets order-critical posets 

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References

  1. 1.
    El-Zahar, M. H. and Schmerl, J. H. (1984) On the size of jump-critical ordered sets, Order 1, 3-5.Google Scholar
  2. 2.
    El-Zahar, M. H. and Rival, I. (1985) Examples of jump-critical ordered sets, SIAM J. Algebraic Discrete Methods 6(4), 713-720.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Mohamed H. El-Zahar
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceAin Shams University, AbbaseiaCairoEgypt

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