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Shelley, Katherine

doi:10.31979/etd.44b5-sg2f

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“…We thank Katherine Shelley Nolan for the use of material in her master's thesis [28] (later incorporated into [26]) that greatly helped to improve the exposition in this paper. We also thank Pomona College, MSRI, and IPM (Tehran), each of which supported visits from some subset of the authors during the development and writing of this paper.…”

Section: Acknowledgementsmentioning

confidence: 99%

Methods for nesting rank 3 normalized matching rank-unimodal posets

Hsu

Logan

Shahriari

2009

Discrete Mathematics

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a b s t r a c tAnderson 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.

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Section: Acknowledgementsmentioning

confidence: 99%