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In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D.

Proceedings of the American Mathematical Society, Vol. 140, No. 11 (NOVEMBER 2012), pp. 3749-3760 (12 pages) In this paper, we will give a recursion formula for double Hurwitz numbers by the cut-join ...