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On the size of jump-critical ordered sets

✍ Scribed by M. H. El-Zahar; J. H. Schmerl

Publisher
Springer Netherlands
Year
1984
Tongue
English
Weight
150 KB
Volume
1
Category
Article
ISSN
0167-8094

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✦ Synopsis

The maximum size of a jump-critical ordered set with jump-number m is at most (m + l)! AMS (MOS) subject classifications (1980). Primary 06AlO; secondary 68C25.

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On minimizing jumps for ordered sets
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✍ Ahmad H. Sharary; Nejib Zaguia πŸ“‚ Article πŸ“… 1991 πŸ› Springer Netherlands 🌐 English βš– 383 KB

An ordered set P is called K-free if it does not contain a four-element subset {a, b, c, d} such that a <b is the only comparability among these elements. In this paper we present a polynomial algorithm to find the jump number of K-free ordered sets. AMS subject classifications (1980). 06Al& &X15.

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A critical set C of order n is a partial latin square of order n which is uniquely completable to a latin square, and omitting any entry of the partial latin square destroys this property. The size s(C) of a critical set C is the number of filled cells in the partial latin square. The I size of a mi