Multiple analogues of binomial coefficients and related families of special numbers

Details Multiple analogues of binomial coefficients and related families of special numbers Multiple analogues of binomial coefficients and related families of special numbers

2010-01-20

arxiv.org/abs/1001.3466v1

Mathematics

Combinatorics

27 pages

Scientific paper

We construct multiple $qt$-binomial coefficients and related multiple analogues of several celebrated families of special numbers in this paper. These multidimensional generalizations include the first and the second kind of $qt$-Stirling numbers, $qt$-Bell numbers, $qt$-Bernoulli numbers, $qt$-Catalan numbers and the $qt$--Fibonacci numbers. In the course of developing main properties of these extensions, we prove results that are significant in their own rights such as certain probability measures on the set of integer partitions.

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