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The Meander Determinant and Its Generalizations

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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.

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References

  1. V. I. Arnold, The branched covering of CP2S 4, hyperbolicity and projective topology, Siberian Math. J. 29 (1988), No. 5, 717–726.

    Article  MathSciNet  Google Scholar 

  2. P. Di Francesco, SU(n) meander determinants, J. Math. Phys. 38 (1997), No. 11, 5905–5943, hep-th/9702181.

    Article  MathSciNet  ADS  Google Scholar 

  3. P. Di Francesco, Meander determinants, Commun. Math. Phys. 191 (1998), No. 3, 543–583, hep-th/9612026.

    Article  ADS  MATH  Google Scholar 

  4. 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.

    Article  MATH  Google Scholar 

  5. 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.

    Article  ADS  Google Scholar 

  6. P. Hanlon and D. Wales, On the decomposition of Brauer’s centralizer algebras, J. Algebra 121 (1989), No. 2, 409–445.

    Article  MathSciNet  MATH  Google Scholar 

  7. 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.

    Article  MathSciNet  MATH  Google Scholar 

  8. K. H. Ko and L. Smolinsky, A combinatorial matrix in 3-manifold theory, Pacific Math. J. 149 (1991), No. 2, 319–336.

    Article  MathSciNet  MATH  Google Scholar 

  9. S. K. Lando and A. K. Zvonkin, Meanders, Selecta Math. Soviet. 11 (1992), No. 2, 117–144.

    MathSciNet  MATH  Google Scholar 

  10. S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Theoret. Comput. Sci. 117 (1993), No. 1-2, 227–241.

    Article  MathSciNet  MATH  Google Scholar 

  11. W. Lunnon, A map-folding problem, Math. Comp. 22 (1968), 193–199.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Martin, Potts Models and Related Problems in Statistical Mechanics, Ser. Adv. Statist. Mech., Vol. 5, World Scientific, River Edge, NJ, 1991.

    Google Scholar 

  13. 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.

    Google Scholar 

  14. 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.

    Google Scholar 

  15. 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.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. J. Touchard, Contributions à l’étude du problème des timbres poste, Canad. J. Math. 2 (1950), 385–398.

    Article  MathSciNet  MATH  Google Scholar 

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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

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  • 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

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