Abstract
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 p P ( n ) / M ( n ) and M ( n ) / p ( n ) tend to zero as n goes to infinity, where p P ( n ) 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.
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