Methods for nesting rank 3 normalized matching rank-unimodal posets

Tim Hsu, Mark J. Logan, Shahriar Shahriari

Research output: Contribution to journalArticlepeer-review

3 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


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