Mappings related to permutations

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Abstract

For each permutation of an interval of integers, a mapping is constructed with certain properties. Even for the infinite intervals N or Z, the result is constructive and easily implemented. A second algorithm is given and utilized to describe the resulting mapping for permutations of a particularly regular type. The question of existence of these mappings arises in proving that certain integral conditions imply various smoothness properties.

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The first author's research reported here was supported in part by NSF Grant MPS 72–04372 A02 and by a fellowship from the Alfred P. Sloan Foundation. The second author's research was supported in part by NSF Grant GP38876.