T-Tetrominos in Arithmetic Progression

2022/07/01 by Emily Feller, Feller, Emily, Robert Hochberg +1
Computer Science · Materials Science · Mathematics · #05B45 #05D10 #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2207.00533

openalex publication_date 2022/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A famous result of D. Walkup is that an m× n rectangle may be tiled by T-tetrominos if and only if both m and n are multiples of 4. The "if" portion may be proved by tiling a 4× 4 block, and then copying that block to fill the rectangle; but, this leads to regular, periodic tilings. In this paper we investigate how much "order" must be present in every tiling of a rectangle by T-tetrominos, where we measure order by length of arithmetic progressions of tiles.

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