• Corpus ID: 18176187

Meander Determinants

@inproceedings{Francesco1996MeanderD,
  title={Meander Determinants},
  author={Philippe Di Francesco},
  year={1996}
}
We prove a determinantal formula for quantities related to the problem of enumeration of (semi-) meanders, namely the topologically inequivalent planar configurations of non-self-intersecting loops crossing a given (half-) line through a given number of points. This is done by the explicit Gram-Schmidt orthogonalization of certain bases of subspaces of the Temperley-Lieb algebra. 
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References

SHOWING 1-10 OF 14 REFERENCES
Meanders and the Temperley-Lieb algebra
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
INTEGRABLE LATTICE MODELS, GRAPHS AND MODULAR INVARIANT CONFORMAL FIELD THEORIES
We review the construction of integrable height models attached to graphs, in connection with compact Lie groups. The continuum limit of these models yields conformally invariant field theories. A
A combinatorial matrix in $3$-manifold theory.
In this paper we study the matrix A(n) which was defined by W. B. R. Lickorish [3]. We prove a result required by Lickorish which completes his topological and combinatorial approach to the
Meander, Folding and Arch Statistics
The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particular
Strings, Matrix Models, and Meanders
Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
  • H. Temperley, E. Lieb
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1971
A transfer-matrix approach is introduced to calculate the 'Whitney polynomial’ of a planar lattice, which is a generalization of the ‘percolation’ and ‘colouring’ problems. This new approach turns
Sorting Jordan Sequences in Linear Time Using Level-Linked Search Trees
TLDR
This paper describes an O(n)-time algorithm for recognizing and sorting Jordan sequences that uses level-linked search trees and a reduction of the recognition and sorting problem to a list-splitting problem.
A map-folding problem
Introduction. In how many ways can a map be folded up? What follows is restricted to the one-dimensional problem, that is: Given a plane chain ('map') of p equal segments ('leaves') jointed together,
Science Selecta Math. Sov
  • Science Selecta Math. Sov
  • 1992
POTTS MODELS AND RELATED PROBLEMS IN STATISTICAL MECHANICS
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