A parameterized formulation for the maximum number of runs problem

A parameterized approach to the problem of the maximum number of runs in a string was introduced by Deza and Franek. In the approach referred to as the d-step approach, in addition to the usual parameter the length of the string, the size of the string's alphabet is considered. The behaviour of the function ρd(n), the maximum number of runs over all strings of length n with exactly d distinct symbols, can be handily expressed in the terms of …