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A note on baxter's generalization of the temperley-lieb operators

  • H. N. V. Temperley
  • D. G. Rogers
Contributed Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 686)

Abstract

The number b(n) of modes of connections of 2n points permissible under Baxter's generalization of the Temperley-Lieb operators is found to be Open image in new window

In particular b(n) differs from the Schröder number sn for n ⩾ 4.

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References

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    R. Baxter, private communicationGoogle Scholar
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    L. Comtet, Advanced Combinatories D. Reidel, Dovdrecht (1974)CrossRefGoogle Scholar
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    J. Riordan ‘The distribution of crossings of chords joining pairs of 2n points on a circle', Mathematics of Computation, 29 (1975), 215–222MathSciNetzbMATHGoogle Scholar
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    D.G. Rogers, ‘The enumeration of a family of ladder graphs Part I. Connective relations', Quart.J.Math. Oxford (2), (to appear)Google Scholar
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    D.G. Rogers, ‘The enumeration of a family of ladder graphs Part II. Schröder relations', (submitted).Google Scholar
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    D.G. Rogers and L.W. Shapiro, 'some correspondences involving the Schröder numbers and relations', Proceedings of International Conference on Combinatorial theory, Canberra (1977) (to appear).Google Scholar
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    N.J.A. Sloane, ‘A handbook of integer sequences’ Academic Press, New York (1973)zbMATHGoogle Scholar
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    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. Ser.A., 322 (1971), 251–280MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    E.T. Whittaker and G.N. Watson, ‘A course of modern analysis’ 4th ed. C.U.P., Cambridge (1950).Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • H. N. V. Temperley
    • 1
  • D. G. Rogers
    • 2
    • 3
  1. 1.Department of Applied MathematicsUniversity CollegeSwanseaUK
  2. 2.Mathematical InstituteOxfordEngland
  3. 3.Department of MathematicsUniversity of Western AustraliaAustralia

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