Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type

TL;DR

This paper presents an automated method to solve combinatorial problems involving counting specific string patterns, demonstrated on a problem from Richard Stanley's American Mathematical Monthly, applicable to various alphabet sizes and string lengths.

Contribution

The authors develop a general automated approach for solving pattern-counting problems in strings, extending beyond a specific case to a broad class of similar problems.

Findings

Successfully automated the proof of Stanley's problem.

Method applies to arbitrary alphabet sizes and string lengths.

Demonstrates versatility in solving pattern occurrence problems.

Abstract

Richard Stanely proposed, in a recent Amer. Math. Monthly Problem, to prove a nice explicit formula for the generating function for the number of n-letter words in {H,T} that have as many occurrences of HT as HH. In this article, we show how to prove this problem automatically, and ANY problem of that type, regardless of the size of the alphabet and the length of the two chosen strings