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PUNCTURED INTERVALS TILE Z 3
Author(s) -
Cambie Stijn
Publication year - 2021
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12085
Subject(s) - tile , mathematics , conjecture , combinatorics , upper and lower bounds , genus , discrete mathematics , mathematical analysis , botany , archaeology , geography , biology
Extending the methods of Metrebian (2018), we prove that punctured intervals tile Z 3 . This solves two questions of Metrebian and completely resolves a question of Gruslys, Leader and Tan. We also pose a question that asks whether there is a relation between the genus g (number of holes) in a one‐dimensional tile T and a uniform bound d such that T tiles Z d . An affirmative answer would generalize a conjecture of Gruslys, Leader and Tan (2016).