Diagonal forms of incidence matrices associated with t-uniform hypergraphs

We consider integer matrices Nt(h) whose rows are indexed by the t-subsets of an n-set and whose columns are all images of a particular column h under the symmetric group Sn. Earlier work has determined a diagonal form for Nt(h) when h has at least t 'isolated vertices' and the results were applied to the binary case of a zero-sum Ramsey-type problem of Alon and Caro involving t-uniform hypergraphs. This paper deals with the case that h does not have as many as t isolated vertices.