Binomial collisions and near collisions
Aart Blokhuis, Andries Brouwer, Benne de Weger
TL;DR
This paper introduces efficient algorithms for finding equal or nearly equal binomial coefficients, provides a conjecturally complete list of cases where they differ by one, and presents new identities for binomial coefficients.
Contribution
It offers novel algorithms for binomial coefficient comparisons, a comprehensive conjectural list of near-equality cases, and new identities, advancing combinatorial mathematics.
Findings
Algorithms for binomial coefficient comparisons
Complete list of cases where coefficients differ by 1 (conjectural)
New identities involving binomial coefficients
Abstract
We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for binomial coefficients that seem to be new.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Advanced Combinatorial Mathematics · Geometric and Algebraic Topology