The generalized Füredi conjecture holds for finite linear lattices Original Research Article

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 image has a partition into image chains such that the sizes of the chains are one of two consecutive integers. In particular, there exists a partition of the linear lattices image (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 image and the sizes of the chains are one of two consecutive integers.