Base-$b$ analogues of classic combinatorial objects
  We study the properties of the base-$b$ binomial coefficient defined by Jiu and the second author, 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. 
Tanay Wakhare, Christophe Vignat
math.NT math.CO