Indefinite Summation and the Kronecker Delta
Dexter C. Kozen, Marc Timme · eCommons (Cornell University) · 2007
Indefinite summation, together with a generalized version of the Kro-necker 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 prop-erties 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. 1