Abstract
The maximum size of a jump-critical ordered set with jump-number m is at most (m+1)!
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References
CheinM. and HabibM.: 1980, The jumps number of dags and posets: An Introduction, Ann. Discrete Math. 9, 189–194.
CogisO. and HabibM.: 1979, Nombre de sauts et graphes série-parallèles, RAIRO Inform. Théor. 13, 3–18.
DilworthR. P.: 1950, A Decomposition Theorem for Partially Ordered Sets, Ann. Math. 51, 161–166.
DuffusD., RivalI. and WinklerP.: 1982, Minimizing Setups for Cycle-Free Ordered Sets, Proc. Amer. Math. Soc. 85, 509–513.
Pulleyblank, W. R.: On Minimizing Setups in Precedence Constrained Scheduling, Discrete Appl. Math. (to appear).
Rival, I.: Optimal Linear Extensions by Interchanging Chains, Proc. Amer. Math. Soc. (to appear).
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Communicated by I. Rival
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El-Zahar, M.H., Schmerl, J.H. On the size of jump-critical ordered sets. Order 1, 3–5 (1984). https://doi.org/10.1007/BF00396268
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DOI: https://doi.org/10.1007/BF00396268