A variation on bisecting the binomial coefficients

TL;DR

This paper introduces an algorithm to find all bisections of binomial coefficients, providing comprehensive results up to n=154, and discusses the likelihood of trivial solutions.

Contribution

The paper presents a novel algorithm for identifying all binomial coefficient bisections and offers extensive data for n up to 154, connecting with prior research.

Findings

Complete table of bisections for n ≤ 154

Conjecture that trivial solutions occur with probability 5/6

Connections established with previous related work

Abstract

In this paper, we present an algorithm which allows us to search for all the bisections for the binomial coefficients $\{\binom{n}{k} \}_{k=0,...,n}$ and include a table with the results for all $n\le 154$. Connections with previous work on this topic is included. We conjecture that the probability of having only trivial solutions is $5/6$. \end{abstract}