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Multiplicities of Integer Arrays
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Lane Clark
Published/Copyright:
May 31, 2010
Abstract
We prove a general theorem about the multiplicity of the entries in certain integer arrays which is best possible in general. As an application we give non-trivial bounds for the multiplicities of several well-known combinatorial arrays including the binomial coefficients, Narayana numbers and the Eulerian numbers. For the binomial coefficients we obtain the result of Singmaster [Amer. Math. Mon. 78: 385–386, 1971].
Keywords.: Multiplicities; integer arrays
Received: 2009-05-17
Accepted: 2009-12-28
Published Online: 2010-05-31
Published in Print: 2010-May
© de Gruyter 2010
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Articles in the same Issue
- Recounting the Number of Rises, Levels, and Descents in Finite Set Partitions
- Multiplicities of Integer Arrays
- Adjugates of Diophantine Quadruples
- A Binary Tree Representation for the 2-Adic Valuation of a Sequence Arising From a Rational Integral
- On a Variant of Van Der Waerden's Theorem
- Note on a Result of Haddad and Helou
- Sequences of Density ζ(k) – 1
- Square-Full Divisors of Square-Full Integers
- Lower Bounds for the Principal Genus of Definite Binary Quadratic Forms
