Bisecting binomial coefficients
Combinatorics
2016-10-10 v1
Abstract
In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously unknown) infinite classes of integers which admit nontrivial bisections, and a class with only trivial bisections. As a byproduct of this last construction, we show conjectures Q2 and Q4 of Cusick and Li. We next find several bounds for the number of nontrivial bisections and further compute (using a supercomputer) the exact number of such bisections for n <= 51.
Cite
@article{arxiv.1610.02063,
title = {Bisecting binomial coefficients},
author = {Eugen J. Ionascu and Thor Martinsen and Pantelimon Stanica},
journal= {arXiv preprint arXiv:1610.02063},
year = {2016}
}