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

  • Yu-Lun Chang
  • Wei-Tian Li
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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).

Keywords

Nested chain decomposition Normalized matching posets Griggs nesting conjecture 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Chung Hsing UniversityTaichungTaiwan

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