Methods for nesting rank 3 normalized matching rank-unimodal posets

Tim Hsu, Mark J. Logan, Shahriar Shahriari

    Research output: Contribution to journalArticlepeer-review

    2 Scopus citations


    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
    Issue number3
    StatePublished - Feb 28 2009


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


    Dive into the research topics of 'Methods for nesting rank 3 normalized matching rank-unimodal posets'. Together they form a unique fingerprint.

    Cite this