Diagonal forms of incidence matrices associated with -uniform hypergraphs

We consider integer matrices N t ( 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 S n . Earlier work has determined a diagonal form for N t ( 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.