A nearest integer solution to the longest run of randomly generated words

Abstract

How rare is the event of observing more than a certain number of consecutive and identical letters of any kind somewhere in a randomly generated word? No one can deny that the use of generating functions is crucial for giving answers to questions like this. This paper, however, gives an answer, essentially based on elementary linear algebra. The derived formula is nevertheless simpler, has computational advantages and gives rise to a "nearest integer" representation with an improved analytical range, as compared to earlier results.