Complexity of cutting words on regular tilings
type: Item
instance of: scholarly article
title: Complexity of cutting words on regular tilings
zbMATH Open document ID: 1111.68095
author: Pascal Hubert
author: L. Vuillon
published in: European Journal of Combinatorics
publication date: 2006-12-07T00:00:00Z
review text: The authors study the cutting words, and they investigate cutting lines on a regular tiling by computing the complexity of the infinite cutting word \(u\) and find the complexity of cutting words for each regular tiling by translation of one polyomino. Finally there is shown the complexity of a cutting word \(u\) in a regular tiling with a polyomino \(Q\) which is equal to \(P_n(u)=(p+q-1)n+1\) for all \(n\geq 0\), where \(P_n(u)\) counts the number of distinct factors of length \(n\) of the infinite word \(u\) and where the boundary of \(Q\) is constructed of \(2p\) horizontal and \(2q\) vertical unit segments. But as said in the conclusion, many questions remain open.
reviewed by: Josef Mikeš
Mathematics Subject Classification ID: 68R15
Mathematics Subject Classification ID: 52B20
Mathematics Subject Classification ID: 05B50
zbMATH DE Number: 5077717
zbMATH Keywords: tilings
zbMATH Keywords: polyominoes
zbMATH Keywords: cutting word
MaRDI profile type: Publication
full work available at URL: j.ejc.2005.05.009
OpenAlex ID: W1998376973
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DOI: 10.1016/J.EJC.2005.05.009
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description: scientific article; zbMATH DE number 5077717