Hall's Marriage Theorem and Pawn Diagrams

TL;DR

This paper investigates the application of Hall's Marriage Theorem to pawn diagrams, revealing that only 1 in 23 such diagrams are unreachable when using the theorem.

Contribution

It demonstrates the specific subset of pawn diagrams that can be generated with Hall's Marriage Theorem and quantifies the proportion that are unreachable.

Findings

1 in 23 pawn diagrams are unreachable by the theorem

Hall's Marriage Theorem applies to a subset of pawn diagrams

Quantitative analysis of diagram reachability

Abstract

This paper is concerned with unreachable pawn diagrams and the subset of which can be generated using Hall's Marriage Theorem. The result is 1 in 23 diagrams are unreachable by applying the theorem.