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Incomplete character sums and a special class of permutations

S. D. Cohen, H. Niederreiter, I. E. Shparlinski, M. Zieve (2001)

Journal de théorie des nombres de Bordeaux

We present a method of bounding incomplete character sums for finite abelian groups with arguments produced by a first-order recursion. This method is particularly effective if the recursion involves a special type of permutation called an -orthomorphism. Examples of -orthomorphisms are given.

Increasing integer sequences and Goldbach's conjecture

Mauro Torelli (2006)

RAIRO - Theoretical Informatics and Applications

Increasing integer sequences include many instances of interesting sequences and combinatorial structures, ranging from tournaments to addition chains, from permutations to sequences having the Goldbach property that any integer greater than 1 can be obtained as the sum of two elements in the sequence. The paper introduces and compares several of these classes of sequences, discussing recurrence relations, enumerative problems and questions concerning shortest sequences.

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