On the support size of null designs of finite ranked posets (Q1586352)

Given two ranks \(t \leq k\) of a finite ranked partially ordered set \(P\), it is possible to define a \(0,1\) matrix, called adjacency matrix, with columns indexed by the elements of rank \(k\) and the rows indexed by the elements of rank \(t\). The kernel of this matrix forms a space. The author considers the space of null \(t\)-designs of finite ranked posets, and the number of non-zero entries of non-zero null \(t\)-designs.