A Variation on the Method of Cartier and Foata via Covering Systems for Combinatorial Identities

A new technique for discovering and proving combinatorial identities is introduced. A bridgework showing the connection between this technique and covering systems of congruences is developed. New bijective proofs of the Vandermonde and Saalschütz identities are given and other ʹdiscoveredʹ identities are given as examples of this technique.