On the tiling by translation problem

S. Brlek; X. Provencal; Jean-Marc Fédou

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On the tiling by translation problem

机译：关于平移翻译问题

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摘要

On square or hexagonal lattices, tiles or polyominoes are coded by words. The polyominoes that tile the plane by translation are characterized by the Beauquier-Nivat condition. By using the constant time algorithms for computing the longest common extensions in two words, we provide a linear time algorithm in the case of pseudo-square polyominoes, improving the previous quadratic algorithm of Gambini and Vuillon. We also have a linear algorithm for pseudo-hexagon polyominoes not containing arbitrarily large square factors. The results are extended to more general tiles.

机译：在正方形或六边形格子上，瓷砖或多米诺骨牌由文字编码。通过平移将平面平铺的多米诺骨牌的特征是Beauquier-Nivat条件。通过使用恒定时间算法来计算两个单词中最长的公共扩展名，我们在伪平方多米诺骨牌的情况下提供了线性时间算法，从而改进了先前的Gambini和Vuillon二次算法。对于不包含任意大平方因子的伪六边形多胺，我们也有一个线性算法。结果扩展到更通用的图块。

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《Discrete Applied Mathematics》 |2009年第3期|共12页
作者
S. Brlek; X. Provencal; Jean-Marc Fédou;
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正文语种 eng
中图分类离散数学;
关键词
Tiling polyominoes; Plane tesselation; Longest common extensions;

机译：平铺多氨基酸;平面镶嵌;最长的常用扩展;

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专利

1. Tiling the line with translates of one tile [J] . Yang Wang Inventiones Mathematicae . 1996,第1a3期

机译：平铺一条平铺线
2. CascadeGAN: A category-supervised cascading generative adversarial network for clothes translation from the human body to tiled images [J] . Neurocomputing . 2020,第Mara21期

机译：CascadeGAN：类别监督的级联生成对抗网络，用于将衣服从人体转换为平铺图像
3. Multi-tiling and equidecomposability of polytopes by lattice translates [J] . Lev Nir, Liu Bochen Bulletin of the London Mathematical Society . 2019,第Pta6期

机译：晶格的多平铺和晶片的相互分解性翻译
4. An Optimal Algorithm for Tiling the Plane with a Translated Polyomino [C] . Andrew Winslow International symposium on algorithms and computation . 2015

机译：平移的多米诺骨牌平铺的最佳算法
5. An integer linear programming formulation for tiling large rectangles using 4 x 6 and 5 x 7 tiles. [D] . Dietert, Grant. 2010

机译：用于使用4 x 6和5 x 7瓦片平铺大矩形的整数线性规划公式。
6. Distortion Orientation and Translation Corrections of Tiled EMCCD Detectors for the New Solid State X-ray Image Intensifier (SSXII) [O] . Hidab Hamwi, Joseph W. Lee, Kenneth R. Hoffmann, -1

机译：新型固态X射线图像增强器（SSXII）的平铺EMCCD检测器的失真方向和平移校正
7. Tiling the Line with Translates of One Tile [O] . Jeffrey C. Lagarias, Yang Wang 100

机译：平铺一个图块的平铺线
8. Orbiter thermal pressure drop characteristics for shuttle orbiter thermal protection system components: High density tile, low density tile, densified low density tile, and strain isolation pad [R] . Lawing, P. L., Nystrom, D. M. 1980

机译：航天飞机轨道器热保护系统组件的轨道器热压降特性：高密度瓦片，低密度瓦片，致密低密度瓦片和应变隔离垫

On the tiling by translation problem

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