科研之友
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摘要
Let V be the n-dimensional vector space over the finited field with q elements and L(V) the lattice of subspaces of V ordered by inclusion. Let V-1, V-2,...,V-r be r selected subspaces of V such that {0} = V-0 subset of V-1 subset of (...) subset of V-r = V and dim(V-i) = Sigma(i)(j=1) k(j). Let I-i be a subinterval of [0, k(i)], i = 1,..., r, let I = {I-1,..., I-r}, and let C[n, r, I] = {K epsilon L(V) : dim(K boolean AND V-i) - dim(K boolean AND Vi-1) epsilon I-i, i = 1, 2,..., r}. Then C[n, r, I] is a graded poset. In this paper, using group actions and flow morphisms we show that C[n, r, I] is log concave and has the NM property, which yields that C[n, r, I] has the strong Sperner property and the LYM property.
