Planarity, Symmetry and Counting Tilings

被引：0

作者：

Koko K. Kayibi

S. Pirzada

机构：

[1] Qatar University,Department of Mathematics and Computer Sciences

[2] University of Kashmir,Department of Mathematics

来源：

Graphs and Combinatorics | 2012年 / 28卷

关键词：

T-tetromino; Tiling; 6-Vertex Ice Model; Medial graph; Eulerian orientation; Tutte polynomial; 05C30;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We axiomatize the geometrical properties of T-tetromino to what we call generalised k-T-tetromino. Using this set of axioms, we show that the number of tilings of a 2kn × 2km rectangular region is given by T(Ln,m ; 3, 3) if and only if the tile is a k-T-tetromino. This generalizes a result of Korn and Pak (Theor Comp Sci 319:3–27, 2004).

引用

页码：483 / 497

页数：14

共 6 条

[1]

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[2]

Korn M.(2004)Tilings of rectangles with T-tetrominoes Theor. Comp. Sci. 319 3-27

[3]

Pak I.(1988)On the evaluation at (3,3) of the Tutte polynomial of a graph J. Comb. Theory Ser. B 44 367-372

[4]

Las Vergnas M.(2008)On the number of tilings of the rectangular board with T-tetrominoes Aust. J. Comb. 14 107-114

[5]

Merino C.(1965)Covering a rectangle with T-tetrominoes Amer. Math. Monthly 72 986-988

[6]

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