Spatial equidistribution of combinatorial number schemes

Abstract

In this paper we use a generalized Lucas type congruence for certain combinatorial number schemes to define IFS.We show some distribution properties of these fractals. As an application we prove that the binomial coefficients, the Stirling numbers of the first and second kind as well as the multinomial coefficients are spatially equidistributed in the nonzero residue classes modulo a prime $p$.