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

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Combinatorial Mathematics

Part of the book series: Lecture Notes in Mathematics ((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

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

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References

  1. R. Baxter, private communication

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  2. L. Comtet, Advanced Combinatories D. Reidel, Dovdrecht (1974)

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  3. J. Riordan ‘The distribution of crossings of chords joining pairs of 2n points on a circle', Mathematics of Computation, 29 (1975), 215–222

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  4. D.G. Rogers, ‘The enumeration of a family of ladder graphs Part I. Connective relations', Quart.J.Math. Oxford (2), (to appear)

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  5. D.G. Rogers, ‘The enumeration of a family of ladder graphs Part II. Schröder relations', (submitted).

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  6. 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).

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  7. N.J.A. Sloane, ‘A handbook of integer sequences’ Academic Press, New York (1973)

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  8. 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), 251–280

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  9. E.T. Whittaker and G.N. Watson, ‘A course of modern analysis’ 4th ed. C.U.P., Cambridge (1950).

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University College, Swansea, UK

    H. N. V. Temperley

  2. Mathematical Institute, Oxford, England

    D. G. Rogers

  3. Department of Mathematics, University of Western Australia, Australia

    D. G. Rogers

Authors
  1. H. N. V. Temperley
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  2. D. G. Rogers
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Editor information

D. A. Holton Jennifer Seberry

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© 1978 Springer-Verlag

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Temperley, H.N.V., Rogers, D.G. (1978). A note on baxter's generalization of the temperley-lieb operators. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062548

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  • DOI: https://doi.org/10.1007/BFb0062548

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08953-7

  • Online ISBN: 978-3-540-35702-5

  • eBook Packages: Springer Book Archive

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