This paper presents a new description of the completion of a quasi-uniform frame. The completion is used to extend the notion of the Samuel compactification to quasi-uniform frames.

We describe (reduced) Gröbner bases of the ideal of polynomials over a field, which vanish on the set of characterisic vectors of the complete unifom families ([n] d ). An interesting feature of the results is that they are largely independent of the monomial order selected. The bases depend only on the ordering of the variables. We can thus use past results related to the lex order in the pres...

Using a generalisation of Hamiltonian cycles to uniform hypergraphs due to Katona and Kierstead, we define a new notion of a Hamiltonian decomposition of a uniform hypergraph. We then consider the problem of constructing such decompositions for complete uniform hypergraphs, and describe its relationship with other topics, such as design theory.