English

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.

Keywords

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}
}
R2 v1 2026-06-22T16:13:41.787Z