Multiple analogues of binomial coefficients and families of related special numbers

Multiple q t -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 q t -Stirling numbers, q t -Bell numbers, q t -Bernoulli numbers, q t -Catalan numbers and the q t -Fibonacci numbers. Certain significant applications are also studied including two discrete probability measures on the set of all integer partitions.