A Proof of the Loehr-Warrington Amazing TEN to the Power n Conjecture

TL;DR

This paper proves a specific combinatorial conjecture by demonstrating the existence of certain words over a small alphabet with particular sum and factor constraints, using minimal computational verification.

Contribution

It provides a proof of the Loehr-Warrington Amazing TEN to the Power n Conjecture through computational verification and combinatorial construction.

Findings

Existence of 10^n words over {3, -2} with specified properties

Verification of the conjecture for all n using 30 seconds of Maple computation

Establishment of combinatorial constraints on words with sum zero

Abstract

We prove, via 30 seconds of Maple computation, that there are 10^n words in the alphabet {3,-2} of length 5n, sum 0, and such that every factor that sums to 0 and that starts with a 3 may not be immediately followed by a -2.