Bounds for Combinatorial Types of Non-Attacking Riders

TL;DR

This paper develops bounds for the number of combinatorial types of non-attacking riders on a chessboard, extending understanding beyond small cases and providing tools applicable to any number of riders and moves.

Contribution

It introduces general upper and lower bound functions for the combinatorial types of non-attacking riders, applicable to any q and r.

Findings

Established bounds for non-attacking rider configurations

Extended analysis to cases with larger q and r

Provided a framework for future exact enumeration

Abstract

Given q non-attacking riders with r moves, the number of combinatorial types has not been found for r greater than 2 and q greater than 3. This paper aims to create upper and lower bound functions which can be applied to any q and r, regardless of size.