A Frameless 2-Coloring of the Plane Lattice. Issue 5 (7th December 2021)

• Record Type: Journal Article
• Authors: Kaplan, Craig S.; Shallit, Jeffrey
• Is Part Of: Mathematics magazine. Volume 94:Issue 5(2021)
• Page Start: 353
• Page End: 360
• Publication Date: 2021-12-07
• Subjects: Primary 05B45 -- Secondary 52C20 -- 68R15; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/0025570X.2021.1983340
• Languages: English
• ISSNs: 0025-570X

Abstract

Summary: A picture frame in two dimensions is a rectangular array of symbols, with at least two rows and columns, where the first and last rows are identical, and the first and last columns are identical. If a coloring of the plane lattice has no picture frames, we call it frameless . In this note, we show how to create a simple 2-coloring of the plane lattice that is frameless.