Explicit Asymptotics for Signed Binomial Sums and Applications to the Carnevale-Voll Conjecture
Université de Lyon, CNRS UMR 5208
Université Claude Bernard Lyon 1
Institut Camille Jordan
43 boulevard du 11 novembre 1918
69622 Villeurbanne Cedex
Carnevale and Voll conjectured that
distinct integers. We check the conjecture when either
is small. We investigate the asymptotic
behaviour of the sum when the ratio
goes to infinity. We find an explicit range
on which the conjecture is true. We show that the conjecture is almost
surely true for any fixed r
. For r
close to 1, we give several
explicit intervals on which the conjecture is also true.
Full version: pdf,
Received July 3 2019; revised versions received February 5 2020; February 9 2020; May 27 2020.
Published in Journal of Integer Sequences,
June 10 2020.
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