TY - JOUR
T1 - Methods for nesting rank 3 normalized matching rank-unimodal posets
AU - Hsu, Tim
AU - Logan, Mark J.
AU - Shahriari, Shahriar
PY - 2009/2/28
Y1 - 2009/2/28
N2 - 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.
AB - 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.
KW - Chain decompositions
KW - Griggs nesting conjecture
KW - LYM property
KW - Nested posets
KW - Normalized matching property
UR - http://www.scopus.com/inward/record.url?scp=59649088781&partnerID=8YFLogxK
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U2 - 10.1016/j.disc.2008.07.013
DO - 10.1016/j.disc.2008.07.013
M3 - Article
AN - SCOPUS:59649088781
SN - 0012-365X
VL - 309
SP - 521
EP - 531
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 3
ER -