2016/10/06 by Eugen J. Ionascu, Ionascu, Eugen J., Thor Martinsen +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1610.02063
arxiv created 2016/10/06 · arxiv updated 2016/10/10
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.