2,109,758 research outputs found

### Tournament Sequences and Meeussen Sequences

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

### Cross correlations of Frank sequences and Chu Sequences.

Sets of Frank sequences and Chu sequences are two classes of polyphase sequence with ideal periodic autocorrelation functions, which at the same time have optimum crosscorrelation functions. The authors consider the crosscorrelations of sets of combined Frank/Chu sequences, which contain a larger number of sequences than either of the two constituent sets. It is shown analytically that the crosscorrelations are similar to those of the original sets with one exception, while the autocorrelations remain perfectly impulsiv

### Hoede-sequences

In an attempt to prove the double-cycle-conjecture for cubic graphs,\ud
C. Hoede formulated the following combinatorial problem.\ud
âGiven a partition of {1, 2, . . . , 3n} into n equal classes, is\ud
it possible to choose from each class a number such that\ud
these numbers form an increasing sequence of alternating\ud
parity?U+00e2U+0080?\ud
Let a Hoede-sequence be defined as an increasing sequence of natural\ud
numbers of alternating parity. We determine the average number of\ud
Hoede-sequences w.r.t. arbitrary partitions, and obtain bounds for the\ud
maximum and minimum number of Hoede-sequences w.r.t. partitions\ud
into equal classes.\u

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