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.
Increasing integer sequences and Goldbach’s conjecture / M. Torelli. - In: RAIRO. INFORMATIQUE THEORIQUE ET APPLICATIONS. - ISSN 0988-3754. - 40:2(2006), pp. 107-121.
Increasing integer sequences and Goldbach’s conjecture
M. TorelliPrimo
2006
Abstract
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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