Tanay Wakhare, Christophe Vignat
Published 2016-07-09Version 1
We study the properties of the base-$b$ binomial coefficient defined by Jiu and Vignat, introduced in the context of a digital binomial theorem. After introducing a general summation formula we derive base-$b$ analogues of the Stirling numbers of the second kind, the Fibonacci numbers, and the classical exponential function.
Curious congruences for Fibonacci numbers
On the least common multiple of $q$-binomial coefficients
Congruence classes of 2-adic valuations of Stirling numbers of the second kind
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