Multicolored Simon Newcomb problems (Q1812831)

This paper deals with generating functions for a kind of combinatorial problems known as Simon Newcomb problems. The problems can best be described in terms of shuffling a deck of cards (with certain specifications) and thereafter dividing the deck into piles according to certain rules. The problem is to determine the number of shuffles resulting in \(k+1\) piles. The method used to count these objects consists of mapping the carddeck to a kind of ``multicoloured'' matrices and then counting these matrices.