Counting Unreachable Single-Side Pawn Diagrams with Limitless Captures

TL;DR

The paper introduces Epiphainein, a method to count unreachable pawn diagrams in chess with unlimited moves, demonstrating efficient computation on standard and larger boards.

Contribution

It presents a novel counting method for unreachable pawn configurations in chess, capable of handling unlimited moves and larger board sizes.

Findings

Counts unreachable pawn diagrams in seconds for 8x8 boards

Extends counting capability to 10x10 boards within hours

Demonstrates efficiency of the serial calculation approach

Abstract

Epiphainein counts unreachable single-side pawn diagrams (in chess) where pawns can move forward or diagonally-forward without limit whilst remaining on the board. Epiphainein is a serial calculation and takes a few seconds to calculate the number of unreachable diagrams on a regular 8 x 8 board. With a decent machine it should take roughly 4 hours to calculate the same on a 10 x 10 board.