Mathematics – Number Theory
Scientific paper
2005-06-24
Int. J. Number Theory 2 (2006), no. 4, 499--522.
Mathematics
Number Theory
24 pages, 6 figures
Scientific paper
If A is a set of nonnegative integers containing 0, then there is a unique nonempty set B of nonnegative integers such that every positive integer can be written in the form a+b, where a\in A and b\in B, in an even number of ways. We compute the natural density of B for several specific sets A, including the Prouhet-Thue-Morse sequence, {0} \cup {2^n : n \geq 0}, and random sets, and we also study the distribution of densities of B for finite sets A. This problem is motivated by Euler's observation that if A is the set of n that have an odd number of partitions, then B is the set of pentagonal numbers {n(3n+1)/2 : n \in Z}. We also elaborate the connection between this problem and the theory of de Bruijn sequences and linear shift registers.
Cooper Joshua N.
Eichhorn Dennis
O'Bryant Kevin
No associations
LandOfFree
Reciprocals of Binary Power Series does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Reciprocals of Binary Power Series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reciprocals of Binary Power Series will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-581583