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On the number of distinct multinomial coefficients

✍ Scribed by George E. Andrews; Arnold Knopfmacher; Burkhard Zimmermann

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
147 KB
Volume
118
Category
Article
ISSN
0022-314X

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✦ Synopsis

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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