The recently developed coinductive calculus of streams finds here a further application in enumerative combinatorics. A general methodology is developed to solve a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite (weighted) automaton; (2) the automaton is minimized by means of the quantitative notion of stream bisimulation; (3) the minimized automaton is used to compute an expression (in terms of stream constants and operators) that represents the stream of all counts.

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Rutten, J.J.M.M. (2001). Coinductive counting : bisimulation in enumerative combinatorics. Software Engineering [SEN]. CWI.