Meanders and the Temperley-Lieb algebra

DOI10.1007/BF02885671zbMath0873.05008arXivhep-th/9602025OpenAlexW2090574622MaRDI QIDQ1360563

O. Golinelli, Philippe Di Francesco, Emmanuel Guitter

Publication date: 19 August 1997

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9602025

zbMATH Keywords

random walksbilinear formTemperley-Lieb algebraGram matrixGram determinantmeandersmeander numbers

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Asymptotic enumeration (05A16) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60)

Related Items (34)

Connected components of meanders. I: Bi-rainbow meanders ⋮ Multiple-SLE _κ connectivity weights for rectangles, hexagons, and octagons ⋮ Cycles in random meander systems ⋮ Orthogonal polynomials and Smith normal form ⋮ Coloring random triangulations ⋮ A formula for crossing probabilities of critical systems inside polygons ⋮ The matrix of chromatic joins and the Temperley-Lieb algebra. ⋮ Enumeration of idempotents in planar diagram monoids ⋮ Problems related to type-\(A\) and type-\(B\) matrices of chromatic joins ⋮ Combinatorial point for fused loop models ⋮ Maximal determinant knots ⋮ Use of meanders and train tracks for description of defects and textures in liquid crystals and \(2+1\) gravity ⋮ A Gram determinant for Lickorish's bilinear form ⋮ SU(N) meander determinants ⋮ A functor-valued invariant of tangles ⋮ RNA folding and large \(N\) matrix theory ⋮ Unnamed Item ⋮ Enumerating meandric systems with large number of loops ⋮ Folding and coloring problems in mathematics and physics ⋮ A solution space for a system of null-state partial differential equations. I ⋮ A solution space for a system of null-state partial differential equations. III ⋮ A solution space for a system of null-state partial differential equations. IV ⋮ Combinatorics of the double-dimer model ⋮ The two-boundary Temperley-Lieb algebra. ⋮ Boundary partitions in trees and dimers ⋮ Meanders: A direct enumeration approach ⋮ New integrable lattice models from Fuss-Catalan algebras ⋮ COMBINATORIAL ASPECTS OF ORTHOGONAL GROUP INTEGRALS ⋮ Meanders: Exact asymptotics ⋮ Quantum Knizhnik–Zamolodchikov equation: reflecting boundary conditions and combinatorics ⋮ Combinatorial aspects of boundary loop models ⋮ Decomposition results for Gram matrix determinants ⋮ On the symmetric enveloping algebra of planar algebra subfactors ⋮ Bilinear forms on skein modules and steps in Dyck paths

Cites Work

• Unnamed Item
• Plane and projective meanders
• A combinatorial matrix in 3-manifold theory
• Meander, folding, and arch statistics
• A branched covering of \(CP^ 2\to S^ 4\), hyperbolicity and projectivity topology
• Sorting jordan sequences in linear time using level-linked search trees
• A Map-Folding Problem
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
• Contribution a L'etude Du Probleme Des Timbres Poste
• Strings, matrix models, and meanders

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