Clumsy Packing of Polyominoes in Finite Space

TL;DR

This paper investigates the problem of clumsy packing of polyominoes in finite rectangular spaces, aiming to maximize spacing so that no additional polyomino can be added, considering boundary conditions.

Contribution

It introduces a formal study of clumsy packing for various polyomino shapes within finite boundaries, accounting for boundary effects.

Findings

Characterization of clumsy packing configurations for different polyominoes.

Analysis of boundary effects on packing efficiency.

Potential algorithms for optimal clumsy packing solutions.

Abstract

Clumsy packing is considered an inefficient packing, meaning we find the minimum number of objects we can pack into a space so that we can not pack any more object. Thus we are effectively spacing out the objects as far apart as possible so that we can not fit another object. In this paper we consider clumsy packing of polyominoes in a finite spaces which must consider boundary conditions. We examine rectangle, $L$, $T$, and plus polyominoes of various sizes.