TY - JOUR
T1 - The generalized Füredi conjecture holds for finite linear lattices
AU - Hsu, Tim
AU - Logan, Mark J.
AU - Shahriari, Shahriar
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2006/12/6
Y1 - 2006/12/6
N2 - We say that a rank-unimodal poset P has rapidly decreasing rank numbers, or the RDR property, if above (resp. below) the largest ranks of P, the size of each level is at most half of the previous (resp. next) one. We show that a finite rank-unimodal, rank-symmetric, normalized matching, RDR poset of width w has a partition into w chains such that the sizes of the chains are one of two consecutive integers. In particular, there exists a partition of the linear lattices Ln (q) (subspaces of an n-dimensional vector space over a finite field, ordered by inclusion) into chains such that the number of chains is the width of Ln (q) and the sizes of the chains are one of two consecutive integers.
AB - We say that a rank-unimodal poset P has rapidly decreasing rank numbers, or the RDR property, if above (resp. below) the largest ranks of P, the size of each level is at most half of the previous (resp. next) one. We show that a finite rank-unimodal, rank-symmetric, normalized matching, RDR poset of width w has a partition into w chains such that the sizes of the chains are one of two consecutive integers. In particular, there exists a partition of the linear lattices Ln (q) (subspaces of an n-dimensional vector space over a finite field, ordered by inclusion) into chains such that the number of chains is the width of Ln (q) and the sizes of the chains are one of two consecutive integers.
KW - Chain decompositions
KW - Generalized Füredi conjecture
KW - LYM property
KW - Linear lattices
KW - Normalized matching property
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U2 - 10.1016/j.disc.2005.09.022
DO - 10.1016/j.disc.2005.09.022
M3 - Article
AN - SCOPUS:33750366037
SN - 0012-365X
VL - 306
SP - 3140
EP - 3144
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 23 SPEC. ISS.
ER -