A Lower Bound on the Growth Constant of Polyaboloes on the Tetrakis Lattice

被引：0
|
作者：
Barequet, Gill [1 ]
De, Minati [2 ]
机构：
[1] Technion Israel Inst Technol, Dept Comp Sci, IL-3200003 Haifa, Israel
[2] Indian Inst Technol Delhi, Dept Math, New Delhi, India
来源：
COMPUTING AND COMBINATORICS, COCOON 2019 | 2019年 / 11653卷
关键词：
Lattice animals; Polyaboloes; Concatenation; Growth constant;
D O I：
10.1007/978-3-030-26176-4_2
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
A "lattice animal" is an edge-connected set of cells on a lattice. In this paper we consider the Tetrakis lattice, and provide the first lower bound on lambda(tau), the growth constant of polyaboloes (animals on this lattice), proving that lambda(tau) >= 2.4345. The proof of the bound is based on a concatenation argument and on calculus manipulations. If we also rely on an unproven assumption, which is, however, supported by empirical data, we obtain the conditional slightly-better lower bound 2.4635.
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页码：13 / 24
页数：12
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