### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 15-30 |

Number of pages | 16 |

Journal | Journal of Number Theory |

Volume | 118 |

Issue number | 1 |

DOIs | |

State | Published - May 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Journal of Number Theory*,

*118*(1), 15-30. https://doi.org/10.1016/j.jnt.2005.08.012

}

*Journal of Number Theory*, vol. 118, no. 1, pp. 15-30. https://doi.org/10.1016/j.jnt.2005.08.012

**On the number of distinct multinomial coefficients.** / Andrews, George E.; Knopfmacher, Arnold; Zimmermann, Burkhard.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the number of distinct multinomial coefficients

AU - Andrews, George E.

AU - Knopfmacher, Arnold

AU - Zimmermann, Burkhard

PY - 2006/5/1

Y1 - 2006/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33645946053&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645946053&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2005.08.012

DO - 10.1016/j.jnt.2005.08.012

M3 - Article

AN - SCOPUS:33645946053

VL - 118

SP - 15

EP - 30

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -