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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
