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

VL - 306

SP - 3140

EP - 3144

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 23 SPEC. ISS.

ER -