Multiple analogues of binomial coefficients and families of related special numbers

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