Methods for nesting rank 3 normalized matching rank-unimodal posets

Tim Hsu, Mark J. Logan, Shahriar Shahriari

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    3 Scopus citations

    Abstract

    Anderson and Griggs proved independently that a rank-symmetric-unimodal normalized matching (NM) poset possesses a nested chain decomposition (or nesting), and Griggs later conjectured that this result still holds if we remove the condition of rank-symmetry. We give several methods for constructing nestings of rank-unimodal NM posets of rank 3, which together produce substantial progress towards the rank 3 case of the Griggs nesting conjecture. In particular, we show that certain nearly symmetric posets are nested; we show that certain highly asymmetric rank 3 NM posets are nested; and we use results on minimal rank 1 NM posets to show that certain other rank 3 NM posets are nested.

    Original languageEnglish (US)
    Pages (from-to)521-531
    Number of pages11
    JournalDiscrete Mathematics
    Volume309
    Issue number3
    DOIs
    StatePublished - Feb 28 2009

    Keywords

    • Chain decompositions
    • Griggs nesting conjecture
    • LYM property
    • Nested posets
    • Normalized matching property

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