Spatial equidistribution of combinatorial number schemes

Abstract

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