| Résume | (joint work with Francesco Cavazzani) In how many ways can a positive integer be expressed as a repeated sum of elements of a fixed list of positive integers? Generalizing this question, the vector partition function counts in how may ways a vector with integer coordinates can be written as a linear combination with nonnegative integer coefficients of the elements of a list of vectors with integer coordinates. This function is ``piecewise quasi-polynomial'', and its local pieces generate a module over the Laurent polynomials. We describe this and several related modules and algebras. Then we show that these modules and algebras can be``geometrically realized'' as the equivariant K-theory of some manifolds that have a nice combinatorial description.We also propose a more natural and general notion of duality between these modules, which corresponds to a Poincaré duality-type correspondence for equivariant K-theory. |
