Tilings of Z with multisets of distances

被引：0

作者：

Kupavskii, Andrey ^{[1
]}

Popova, Elizaveta ^{[1
]}

机构：

[1] Moscow Inst Phys & Technol, Moscow, Russia

来源：

DISCRETE MATHEMATICS | 2024年 / 347卷 / 09期

关键词：

Tiling; One-dimensional tiling; INTEGERS;

D O I：

10.1016/j.disc.2024.114053

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study tilings of Z , that is, coverings of Z by disjoint sets (tiles). Let T = { d 1 , ... , d s } be a given multiset of distances. Is it always possible to tile Z by tiles, for which the multiset of distances between consecutive points is equal to T ? In this paper, we give a sufficient condition that such a tiling exists. Our result allows multisets of distances to have arbitrarily many distinct values. Our result generalizes most of the previously known results, all of which dealt with the cases of 2 or 3 distinct distances. (c) 2024 Elsevier B.V. All rights reserved.

引用

页数：9

共 11 条

[1]

Bhattacharya S, 2020, AM J MATH, V142, P255

[2] On Covering by Translates of a Set [J].