The Greatest Common Divisor of Multinomial Coefficients, or A Neat Little Number Theory Result

TL;DR

This paper determines the greatest common divisor of specific multinomial coefficients, linking a number theory problem to characteristic numbers of manifolds, revealing a neat mathematical relationship.

Contribution

It provides a novel explicit formula for the GCD of certain multinomial coefficients, connecting number theory with geometric invariants.

Findings

Explicit formula for the GCD of multinomial coefficients

Connection between number theory and manifold characteristic numbers

Simplification of a previously complex calculation

Abstract

While studying a characteristic number of manifolds we noticed that the calculation was simply computing a multiple of a multinomial coefficient. We were, at the time, interested in computing the greatest common divisor of these characteristic numbers, and from that came this fun and interesting number theory problem. In this short paper, I will give the answer to this problem, which gives the greatest common divisor of certain multinomial coefficients.