Tiling rectangles with holey polyominoes

TL;DR

This paper introduces holey polyominoes with transparent squares, explores their ability to tile rectangles, and categorizes most small cases, advancing understanding of polyomino tiling possibilities.

Contribution

It presents a new class of polyominoes with holes and provides a comprehensive categorization of their tiling capabilities for small cases.

Findings

Most small holey polyominoes can tile rectangles

Six small polyominoes remain unclassified in tiling ability

Holey polyominoes expand the scope of polyomino tiling studies

Abstract

We present a new type of polyominoes that can have transparent squares (holes). We show how these polyominoes can tile rectangles and we categorise them according to their tiling ability. We were able to categorise all but 6 polyominoes with 5 or fewer visible squares.