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math.NT2003
Almost Alternating Sums
Kevin O'Bryant, Bruce Reznick, Monika Serbinowska
Writing for a general mathematical audience, we provide elementary upper and lower bounds on the growth (as a function of N) of the sum \sum_{n=1}^N (-1)^{\floor{n x}} for various…
math.NT2003★ 11 cited
Fraenkel's Partition and Brown's Decomposition
Kevin O'Bryant
Denote the sequence ([ (n-x') / x ])_{n=1}^\infty by B(x, x'), a so-called Beatty sequence. Fraenkel's Partition Theorem gives necessary and sufficient conditions for B(x, x') and…