Tilings of hyperbolic $(2\times n)$-board with colored squares and dominoes

TL;DR

This paper explores the tiling problem using colored squares and dominoes on a hyperbolic (2×n)-board, extending classical Euclidean tiling concepts to hyperbolic geometry.

Contribution

It introduces the first analysis of tilings with colored squares and dominoes on hyperbolic (2×n)-boards, expanding tiling theory into hyperbolic geometries.

Findings

Developed a new tiling model for hyperbolic (2×n)-boards.

Provided enumeration methods for colored tilings.

Extended classical tiling results to hyperbolic settings.

Abstract

Several articles deal with tilings with squares and dominoes of the well-known regular square mosaic in Euclidean plane, but not any with the hyperbolic regular square mosaics. In this article, we examine the tiling problem with colored squares and dominoes of one type of the possible hyperbolic generalization of $(2\times n)$-board.