Mathematics – Combinatorics
Scientific paper
2000-02-25
Electronic Journal of Combinatorics 7(1) (2000) #R44. http://www.combinatorics.org/Volume_7/Abstracts/v7i1r44.html
Mathematics
Combinatorics
16 pages, 1 figure. Minor changes only; final version as published in EJC
Scientific paper
A "tournament sequence" is an increasing sequence of positive integers (t_1,t_2,...) such that t_1=1 and t_{i+1} <= 2 t_i. A "Meeussen sequence" is an increasing sequence of positive integers (m_1,m_2,...) such that m_1=1, every nonnegative integer is the sum of a subset of the {m_i}, and each integer m_i-1 is the sum of a unique such subset. We show that these two properties are isomorphic. That is, we present a bijection between tournament and Meeussen sequences which respects the natural tree structure on each set. We also present an efficient technique for counting the number of tournament sequences of length n, and discuss the asymptotic growth of this number. The counting technique we introduce is suitable for application to other well-behaved counting problems of the same sort where a closed form or generating function cannot be found.
Cook Matthew
Kleber Michael
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