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.Comment: 16 pages, 1 figure. Minor changes only; final version as published in
EJ
