Meanders and the Temperley-Lieb algebra

被引：56

作者：

P. Di Francesco

O. Golinelli

E. Guitter

机构：

[1] C.E.A. Saclay,Service de Physique Théorique

来源：

Communications in Mathematical Physics | 1997年 / 186卷 / 1期

关键词：

Recursion Relation; Marked Point; Final Height; Boltzmann Weight; Open Arch;

D O I：

10.1007/BF02885671

中图分类号：

学科分类号：

摘要：

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 weightq per 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.

引用

页码：1 / 59

页数：58

共 13 条

[1]

Hoffman K.(1986)Sorting Jordan sequences in linear time using level-linked search trees Information and Control 68 170-184

[2]

Mehlhorn K.(1988)The branched covering of Siberian Math. Jour. 29 717-726

[3]

Rosenstiehl P.(1991) → Pacific. J. Math 149 319-336

[4]

Tarjan R.(1993), hyperbolicity and projective topology Theor. Science 117 227-241

[5]

Arnold V.(1950)A combinatorial matrix in 3-manifold theory Canad. J. Math. 2 385-398

[6]

Ko K. H.(1968)Plane and Projective Meanders Math. of Computation 22 193-199

[7]

Smolinsky L.(1971)Contributions à l’étude du problème des timbres poste Proc. Roy. Soc. A322 251-280

[8]

Lando S.(undefined)A map-folding problem undefined undefined undefined-undefined

[9]

Zvonkin A.(undefined)Relations between the percolation and coloring problem and other graph- theoretical problems associated with regular planar lattices: some exact results for the percolation problem undefined undefined undefined-undefined

[10]

Touchard J.(undefined)undefined undefined undefined undefined-undefined

← 1 2 →