Abstract
We investigate various generalizations of meanders, that is, configurations of non-self-intersecting loops crossing a line through a given number of points. In all cases, we derive explicit formulas for corresponding meander determinants.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
V. I. Arnold, The branched covering of CP2 → S 4, hyperbolicity and projective topology, Siberian Math. J. 29 (1988), No. 5, 717–726.
P. Di Francesco, SU(n) meander determinants, J. Math. Phys. 38 (1997), No. 11, 5905–5943, hep-th/9702181.
P. Di Francesco, Meander determinants, Commun. Math. Phys. 191 (1998), No. 3, 543–583, hep-th/9612026.
P. Di Francesco, O. Golinelli, and E. Guitter, Meander, folding and arch statistics, Math. Comput. Modelling 26 (1997), No. 8-10, 97–147, hep-th/9506030.
P. Di Francesco, O. Golinelli, and E. Guitter, Meanders and the Temperley-Lieb algebra, Commun. Math. Phys. 86 (1997), No. 1, 1–59, hep-th/9602025.
P. Hanlon and D. Wales, On the decomposition of Brauer’s centralizer algebras, J. Algebra 121 (1989), No. 2, 409–445.
K. Hoffmann, K. Mehlhorn, P. Rosenstiehl, and R. E. Tarjan, Sorting Jordan sequences in linear time using level-linked search trees, Inform. and Control 68 (1986), No. 1-3, 170–184.
K. H. Ko and L. Smolinsky, A combinatorial matrix in 3-manifold theory, Pacific Math. J. 149 (1991), No. 2, 319–336.
S. K. Lando and A. K. Zvonkin, Meanders, Selecta Math. Soviet. 11 (1992), No. 2, 117–144.
S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Theoret. Comput. Sci. 117 (1993), No. 1-2, 227–241.
W. Lunnon, A map-folding problem, Math. Comp. 22 (1968), 193–199.
P. Martin, Potts Models and Related Problems in Statistical Mechanics, Ser. Adv. Statist. Mech., Vol. 5, World Scientific, River Edge, NJ, 1991.
N. Yu. Reshetikhin, Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links 1 and 2, Tech. Report E-4-87, Steklov Mathematical Institute, St. Petersburg, 1988.
N. Yu. Reshetikhin, Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links 1 and 2, Tech. Report E-17-87, Steklov Mathematical Institute, St. Petersburg, 1988.
H. N. V. Temperley and E. H. Lieb, Relations between the “percolation” and “colouring” problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the “percolation” problem, Proc. Roy. Soc. London, Ser. A 322 (1971), No. 1549, 251–280.
J. Touchard, Contributions à l’étude du problème des timbres poste, Canad. J. Math. 2 (1950), 385–398.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Di Francesco, P. (2000). The Meander Determinant and Its Generalizations. In: van Diejen, J.F., Vinet, L. (eds) Calogero—Moser— Sutherland Models. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1206-5_9
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1206-5_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7043-0
Online ISBN: 978-1-4612-1206-5
eBook Packages: Springer Book Archive