Remarks on recent formulas of Wilson and Frankl (Q1209284)

By a signed \(t\)-design, we mean a collection of sets \(S=S(\lambda,t,k,v)\) with integral multiplicities so that each set in \(S\) is a \(k\)-element subset of a fixed \(v\)-element set \(X\) and so that, for each \(t\)-element subset of \(X\), the multiplicities of the sets in \(S\) containing that \(t\)- subset sum to \(\lambda\). If all of the multiplicities are 1, \(S\) is called a \(t\)-design; if \(\lambda=0\), \(S\) is called a null \(t\)-design. This paper is devoted to proving several structure theorems for the space of null \(t\)-designs and its orthogonal complement.