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On the size of jump-critical ordered sets

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  • 17 Citations


The maximum size of a jump-critical ordered set with jump-number m is at most (m+1)!

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  1. 1.

    CheinM. and HabibM.: 1980, The jumps number of dags and posets: An Introduction, Ann. Discrete Math. 9, 189–194.

  2. 2.

    CogisO. and HabibM.: 1979, Nombre de sauts et graphes série-parallèles, RAIRO Inform. Théor. 13, 3–18.

  3. 3.

    DilworthR. P.: 1950, A Decomposition Theorem for Partially Ordered Sets, Ann. Math. 51, 161–166.

  4. 4.

    DuffusD., RivalI. and WinklerP.: 1982, Minimizing Setups for Cycle-Free Ordered Sets, Proc. Amer. Math. Soc. 85, 509–513.

  5. 5.

    Pulleyblank, W. R.: On Minimizing Setups in Precedence Constrained Scheduling, Discrete Appl. Math. (to appear).

  6. 6.

    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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AMS (MOS) subject classifications (1980)

  • Primary 06A10
  • secondary 68C25

Key words

  • Jump number
  • jump-critical ordered sets