Multiple analogues of binomial coefficients and families of related special numbers

Multiple qtqt-binomial coefficients and multiple analogues of several celebrated families of related special numbers are constructed in this paper. These higher-dimensional generalizations include the first and the second kind of qtqt-Stirling numbers, qtqt-Bell numbers, qtqt-Bernoulli numbers, qtqt-Catalan numbers and the qtqt-Fibonacci numbers. Certain significant applications are also studied including two discrete probability measures on the set of all integer partitions.