CHRISTOFFEL WORDS AND MARKOFF TRIPLES: AN ALGEBRAIC APPROACH

被引：0
|
作者：
Lasnier, Alex [1 ]
机构：
[1] Univ Sherbrooke, Dept Math, Sherbrooke, PQ J1K 2R1, Canada
来源：
COMMUNICATIONS IN ALGEBRA | 2013年 / 41卷 / 03期
关键词：
Christoffel words; Markoff triples; Uniqueness conjecture for Markoff numbers; Representation theory; 16G20; 11D25; 68R15; NUMBERS; UNIQUENESS; FORMS;
D O I：
10.1080/00927872.2011.642044
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce a family of modules, called Markoff modules, generated by a cluster-mutation-like iterative process. We show that these modules are combinatorially similar to Christoffel words. Furthermore, we construct a bijective map between the set of Markoff module triples and the set of proper Markoff triples. This allows us to interpret the uniqueness conjecture for Markoff numbers within an algebraic framework.
引用
收藏
页码：1195 / 1216
页数：22
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