Planarity, Symmetry and Counting Tilings

被引：2

作者：

Kayibi, Koko K. ^{[2
]}

Pirzada, S. ^{[1
]}

机构：

[1] Univ Kashmir, Dept Math, Srinagar 190006, Jammu & Kashmir, India

[2] Qatar Univ, Dept Math & Comp Sci, Doha, Qatar

来源：

GRAPHS AND COMBINATORICS | 2012年 / 28卷 / 04期

关键词：

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

D O I：

10.1007/s00373-011-1062-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 x 2km rectangular region is given by T(L (n,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：15

共 12 条

[1]

Baxter R, 1982, EXACTLY SOLVED MODEL

[2]

Brylawski Thomas, 1992, MATROID APPL, V40, P123

[3]

Golomb S.W., 1995, POLYOMINOES, P97

[4]

Hetyei G., 2009, DMTCS P AK, P479

[5] Tetromino tilings and the Tutte polynomial [J].

Jacobsen, Jesper Lykke .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2007, 40 (07) :1439-1446

[6]

Kayibi K., DISC MATH UNPUB

[7] Tilings of rectangles with T-tetrominoes [J].

Korn, M ;

Pak, I .

THEORETICAL COMPUTER SCIENCE, 2004, 319 (1-3) :3-27

[8]

Korn M., COMBINATORIAL EVALUA

[9]

Merino C, 2008, AUSTRALAS J COMB, V41, P107

[10] ON THE EVALUATION AT (3, 3) OF THE TUTTE POLYNOMIAL OF A GRAPH [J].

VERGNAS, ML .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1988, 45 (03) :367-372

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