Meanders and the Temperley-Lieb algebra

P. Di Francesco, O. Golinelli, E. Guitter

Research output: Contribution to journalArticlepeer-review


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 weight q 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 of q, and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks.

Original languageEnglish (US)
Pages (from-to)1-59
Number of pages59
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - 1997
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Meanders and the Temperley-Lieb algebra'. Together they form a unique fingerprint.

Cite this