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On the number of distinct multinomial coefficients |
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| Authors: | George E. Andrews Arnold Knopfmacher Burkhard Zimmermann |
| Affiliation: | a Mathematics Department, 410 McAllister Building, The Pennsylvania State University, University Park, PA 16802, USA b The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, Johannesburg, South Africa c Research Institute for Symbolic Computation, Johannes Kepler Universität Linz, A-4040 Linz, Austria |
| 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 pP(n)/M(n) and M(n)/p(n) tend to zero as n goes to infinity, where pP(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. |
| Keywords: | Factorials Binomial coefficients Combinatorial functions Partitions of integers Polynomial ideals Grö bner bases |
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