An Explicit Solution to the Chessboard Pebbling Problem

TL;DR

This paper provides exact formulas and asymptotic analysis for the number of reachable configurations in the chessboard pebbling problem, advancing understanding of this combinatorial challenge.

Contribution

It derives explicit expressions for reachable configurations and explores their asymptotic behavior, offering new insights into the problem's structure.

Findings

Exact formulas for G(k) and G(k,m)

Asymptotic limits of configuration counts

Enhanced understanding of the pebbling problem

Abstract

We consider the chessboard pebbling problem analyzed by Chung, Graham, Morrison and Odlyzko [3]. We study the number of reachable configurations $G(k)$ and a related double sequence $G(k,m)$. Exact expressions for these are derived, and we then consider various asymptotic limits.