caa a22 4500 445813911 CHVBK 20180317145220.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s11083-010-9164-2 doi (NATIONALLICENCE)springer-10.1007/s11083-010-9164-2 On Nested Chain Decompositions of Normalized Matching Posets of Rank 3 [Elektronische Daten] [Elinor Escamilla, Andreea Nicolae, Paul Salerno, Shahriar Shahriari, Jordan Tirrell] In 1975, J. Griggs conjectured that a normalized matching rank-unimodal poset possesses a nested chain decomposition. This elegant conjecture remains open even for posets of rank 3. Recently, Hsu, Logan, and Shahriari have made progress by developing techniques that produce nested chain decompositions for posets with certain rank numbers. As a demonstration of their methods, they prove that the conjecture is true for all rank 3 posets of width at most 7. In this paper, we present new general techniques for creating nested chain decompositions, and, as a corollary, we demonstrate the validity of the conjecture for all rank 3 posets of width at most 11. Springer Science+Business Media B.V., 2010 Chain decompositions nationallicence Nested posets nationallicence Griggs nesting conjecture nationallicence Normalized matching property nationallicence LYM property nationallicence Saturated partition nationallicence Escamilla Elinor Department of Mathematics, Pomona College, 91711, Claremont, CA, USA aut Nicolae Andreea Department of Mathematics, Pomona College, 91711, Claremont, CA, USA aut Salerno Paul Department of Mathematics, Pomona College, 91711, Claremont, CA, USA aut Shahriari Shahriar Department of Mathematics, Pomona College, 91711, Claremont, CA, USA aut Tirrell Jordan Department of Mathematics, Lafayette College, 18042, Easton, PA, USA aut Order Springer Netherlands 28/2(2011-07-01), 357-373 0167-8094 28:2<357 2011 28 11083 https://doi.org/10.1007/s11083-010-9164-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11083-010-9164-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Escamilla Elinor Department of Mathematics, Pomona College, 91711, Claremont, CA, USA aut NATIONALLICENCE 700 1- Nicolae Andreea Department of Mathematics, Pomona College, 91711, Claremont, CA, USA aut NATIONALLICENCE 700 1- Salerno Paul Department of Mathematics, Pomona College, 91711, Claremont, CA, USA aut NATIONALLICENCE 700 1- Shahriari Shahriar Department of Mathematics, Pomona College, 91711, Claremont, CA, USA aut NATIONALLICENCE 700 1- Tirrell Jordan Department of Mathematics, Lafayette College, 18042, Easton, PA, USA aut NATIONALLICENCE 773 0- Order Springer Netherlands 28/2(2011-07-01), 357-373 0167-8094 28:2<357 2011 28 11083 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer