On the number of distinct multinomial coefficients Original Research Article

We study M(n), the number of distinct values taken by multinomial coefficients with upper entry n, and some closely related sequences. We show that both image and M(n)/p(n) tend to zero as n goes to infinity, where image is the number of partitions of n into primes and p(n) is the total number of partitions of n. To use methods from commutative algebra, we encode partitions and multinomial coefficients as monomials.