Combinatorial Analysis of Integer Power Product Expansions
نویسنده
چکیده
Let f (x) = 1+ ∑n=1 anx n be a formal power series with complex coefficients. Let {rn}n=1 be a sequence of nonzero integers. The Integer Power Product Expansion of f (x), denoted ZPPE, is ∏k=1(1+wkx k)rk . Integer Power Product Expansions enumerate partitions of multi-sets. The coefficients {wk}k=1 themselves possess interesting algebraic structure. This algebraic structure provides a lower bound for the radius of convergence of the ZPPE and provides an asymptotic bound for the weights associated with the multi-sets.
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