On tilings by ribbon tetrominoes
type: Item
instance of: scholarly article
title: On tilings by ribbon tetrominoes
zbMATH Open document ID: 0936.05030
author: Roman Muchnik
author: Igor Pak
published in: Journal of Combinatorial Theory. Series A
publication date: 1999-12-20T00:00:00Z
review text: The paper is on tilings of regions using ribbon tetrominoes. A ribbon tetromino is a polyomino having 4 squares \((i,j)\) and at most one square in every diagonal \((i-j= c)\). There are 8 of these ribbon tetrominoes. If one studies tilings of simply connected regions \(T\) using these 8 objects the numbers \(a_1(T),\dots, a_8(T)\) of tetrominoes used can vary for different tilings of the same region, nevertheless certain relations between these numbers remain invariant and hence are connected to the region. The authors have found some of these relations and prove them by studying the Cayley graph of a certain group, introducing weights for the cells in this graph and calculating winding numbers connected to the closed path in the graph related to the simply connected region. The given invariants turn out to be equal to these winding numbers and hence are invariant.
Mathematics Subject Classification ID: 05B50
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1356443
zbMATH Keywords: tilings
zbMATH Keywords: ribbon tetrominoes
zbMATH Keywords: polyomino
zbMATH Keywords: winding numbers
reviewed by: Herman J. Tiersma
MaRDI profile type: Publication
OpenAlex ID: W1996762867
cites work: Tiling with polyominoes and combinatorial group theory
cites work: A note on tiling with integer-sided rectangles
cites work: A Pedestrian Approach to a Method of Conway, or, A Tale of Two Cities
cites work: Conway's Tiling Groups
cites work: Covering a Rectangle with T-Tetrominoes
DOI: 10.1006/JCTA.1999.2980
description: scientific article; zbMATH DE number 1356443