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Some Remarks on Nestings in the Normalized Matching Posets of Rank 3

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Abstract

In 1970s, Griggs conjectured that every normalized matching rank-unimodal poset has a nested chain decomposition. This conjecture is proved to be true only for some posets of small ranks (Wang Discrete Math. 145(3), 493–497, 2005; Hsu et al. Discrete Math. 309(3), 521–531, 2009; Escamilla et al. Order 28, 357–373, 2011). In this paper, we provide some sufficient conditions on the rank numbers of posets of rank 3 to satisfy the Griggs’s conjecture by refining the proofs in the two papers (Hsu et al. Discrete Math. 309(3), 521–531, 2009; Escamilla et al. Order 28, 357–373, 2011).

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Authors and Affiliations

  1. Department of Applied Mathematics, National Chung Hsing University, Taichung, 40227, Taiwan

    Yu-Lun Chang & Wei-Tian Li

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  1. Yu-Lun Chang
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  2. Wei-Tian Li
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Correspondence to Wei-Tian Li.

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Supported by MOST-105-2115-M-005-003-MY2.

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Chang, YL., Li, WT. Some Remarks on Nestings in the Normalized Matching Posets of Rank 3. Order 36, 501–505 (2019). https://doi.org/10.1007/s11083-018-9479-y

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  • DOI: https://doi.org/10.1007/s11083-018-9479-y

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