Published online by Cambridge University Press: 20 July 2006
Increasing integer sequences include many instances of interestingsequences and combinatorial structures, ranging from tournaments to additionchains, from permutations to sequences having the Goldbach property that any integer greater than 1 can be obtained as the sum of two elementsin the sequence. The paper introduces and compares several of these classesof sequences, discussing recurrence relations, enumerative problems andquestions concerning shortest sequences.