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Decompositions of partially ordered sets into chains and antichains of given size

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Abstract

Every partially ordered set P on at least (1+o(1))n 3 elements can be decomposed into subposets of size n that are ‘almost’ chains or antichains. This lower bound on P is asymptotically best possible. Similar results are presented for other types of combinatorial structures.

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Authors and Affiliations

  1. School of Mathematics, Tel Aviv University, Israel

    Yair Caro

  2. Computer and Automation Institute, Kende u. 13-17, H-1111, Budapest, Hungary

    Zsolt Tuza

Authors
  1. Yair Caro
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  2. Zsolt Tuza
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Communicated by I. Rival

Research supported in part by the ‘AKA’ Research Fund of the Hungarian Academy of Sciences, grant 1-3-86-264.

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Caro, Y., Tuza, Z. Decompositions of partially ordered sets into chains and antichains of given size. Order 5, 245–255 (1988). https://doi.org/10.1007/BF00354892

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  • DOI: https://doi.org/10.1007/BF00354892

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