Dexter Kozen and Marc Timme. Indefinite summation and the Kronecker delta. Technical Report http://hdl.handle.net/1813/8352, Computing and Information Science, Cornell University, October 2007.

Indefinite summation, together with a generalized version of the Kronecker delta, provide a calculus for reasoning about various polynomial functions that arise in combinatorics, such as the Tutte, chromatic, flow, and reliability polynomials. In this paper we develop the algebraic properties of the indefinite summation operator and the generalized Kronecker delta from an axiomatic viewpoint. Our main result is that the axioms are equationally complete; that is, all equations that hold under the intended interpretations are derivable in the calculus.