Methods for nesting rank 3 normalized matching rank-unimodal posets |
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Authors: | Tim Hsu |
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Institution: | a Department of Mathematics, San José State University, San José, CA 95192-0103, USA b Division of Science and Mathematics, University of Minnesota-Morris, Morris, MN 56267, USA c Department of Mathematics, Pomona College, Claremont, CA 91711, USA |
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Abstract: | 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. |
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Keywords: | Chain decompositions Nested posets Griggs nesting conjecture Normalized matching property LYM property |
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