Perfect precise colorings of plane semiregular tilings.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2023-09-01 DOI:10.1107/S2053273323006630

Manuel Joseph C Loquias, Rovin B Santos

引用次数: 0

Abstract

A coloring of a planar semiregular tiling {\cal T} is an assignment of a unique color to each tile of {\cal T}. If G is the symmetry group of {\cal T}, the coloring is said to be perfect if every element of G induces a permutation on the finite set of colors. If {\cal T} is k-valent, then a coloring of {\cal T} with k colors is said to be precise if no two tiles of {\cal T} sharing the same vertex have the same color. In this work, perfect precise colorings are obtained for some families of k-valent semiregular tilings in the plane, where k ≤ 6.

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完美精确的平面半规则瓷砖着色。

平面半正则平铺{\ \ T}的上色是对{\ \ T}的每个平铺{\ \ T}的一个唯一的颜色赋值。如果G是{\cal T}的对称群，则如果G的每个元素在颜色的有限集合上引起一个排列，则称该着色是完全的。如果{\cal T}是k价的，那么如果{\cal T}的两个砖块共用同一个顶点，没有相同的颜色，那么用k种颜色对{\cal T}着色就是精确的。本文在k≤6的平面上，得到了若干k价半正则铺层族的完美精确着色。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.