TESSELLATION AND G-TESSELLATION OF CIRCULANTS, Q(6), AND Q(6)(T)

Let C subset of or equal to R(n) be a pointed cone generated by ration al vectors. A subset H of integral vectors in C is said to be a Hilber t basis for C if all integer vectors in C can be expressed as nonnegat ive integer combinations of vectors in H. A tessellation of C is a par tition of C into unimodular subcones whose generators are from H. The existence of such a tessellation has consequences similar to Caratheod ory's theorem in linear algebra. It is an open question whether such a tessellation exists for all C. In this paper we show that tessellatio n (or its generalization) exists for cones generated by circulant matr ices, Q(6), and Q(6)(t).