Bishop Independence on the Surface of a Square Prism

TL;DR

This paper solves the bishop independence problem for all square prism surface sizes, establishing the maximum number of non-attacking bishops that can be placed on such surfaces.

Contribution

It provides a complete solution to the bishop independence problem specifically for the surface of square prisms, a previously unaddressed geometric configuration.

Findings

Determined the bishop independence number for all square prism surface sizes.

Established formulas or bounds for non-attacking bishop placements.

Extended bishop independence concepts to non-flat, three-dimensional surfaces.

Abstract

Bishop independence concerns determining the maximum number of bishops that can be placed on a board such that no bishop can attack any other bishop. This paper presents the solution to the bishop independence problem, determining the bishop independence number, for all sizes of boards on the surface of a square prism.