Meanders and the Temperley-Lieb algebra
Meanders and the Temperley-Lieb algebra
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Meanders 和 Temperley-Lieb 代数
DOI：
10.1007/bf02885671
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发表时间：
1996
影响因子：
2.4
通讯作者：
E. Guitter
中科院分区：
文献类型：
--
作者：
P. Francesco;O. Golinelli;E. Guitter
研究了与Temperley-Lieb代数有关的曲折的统计。每个（多分量）曲折对应于代数的一对简化元素。的weightqper连接组件的曲折的分配转化为代数上的双线性形式，与一个革兰氏矩阵编码的曲折数的精细结构。在这里，我们计算相关联的革兰行列式作为一个函数ofq，并利用正交化过程中推导出的曲折数的替代表达式作为相关的随机游动的总和。
The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weightqper connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram determinant as a function ofq, and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks.