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The asymptotic diameter of cyclohedra

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Abstract

It is shown here that the diameter of the d-dimensional cyclohedron is not greater than ⌈5d/2⌉ − 2. It is also shown that the 5/2 coefficient in this upper bound is asymptotically sharp. More precisely, the d-dimensional cyclohedron has diameter at least \(5d/2 - 4\sqrt d - 4\) .

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References

  1. R. Bott and C. Taubes, On the self-linking of knots, Journal of Mathematical Physics 35 (1994), 5247–5287.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. P. Carr and S. L. Devadoss, Coxeter complexes and graph-associahedra, Topology and its Applications 153 (2006), 2155–2168.

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Ceballos and V. Pilaud, The diameter of type D associahedra and the non-leaving-face property, European Journal of Combinatorics 51 (2016), 109–124.

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Chapoton, S. Fomin and A. Zelevinsky, Polytopal realizations of generalized associahedra, Canadian Mathematical Bulletin 45 (2002), 537–566.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. A. De Loera, J. Rambau and F. Santos, Triangulations: Structures for Algorithms and Applications, Algorithms and Computation in Mathematics, Vol. 25, Springer, Berlin, 2010.

    Book  MATH  Google Scholar 

  6. S. L. Devadoss, A realization of graph associahedra, Discrete Mathematics 309 (2009), 271–276.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Fomin and A. Zelevinsky, Y-systems and generalized associahedra, Annals of Mathematics 158 (2003), 977–1018.

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Markl, Simplex, associahedron, and cyclohedron, in Higher Homotopy Structures in Topology and Mathematical Physics, Contemporary Mathematics, Vol. 227, American Mathematical Society, Providence, RI, 1999, pp. 235–265.

    Chapter  Google Scholar 

  9. L. Pournin, The diameter of associahedra, Advances in Mathematics 259 (2014), 13–42.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Rambau, Triangulations of cyclic polytopes and higher Bruhat orders, Mathematika 44 (1997), 162–194.

    Article  MathSciNet  MATH  Google Scholar 

  11. R. Simion, A type-B associahedron, Advances in Applied Mathematics 30 (2003), 2–25.

    Article  MathSciNet  MATH  Google Scholar 

  12. D. Sleator, R. Tarjan and W. Thurston, Rotation distance, triangulations, and hyperbolic geometry, Journal of the American Mathematical Society 1 (1988), 647–681.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. LIPN, Université Paris 13, Villetaneuse, France

    Lionel Pournin

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  1. Lionel Pournin
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Correspondence to Lionel Pournin.

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Research funded by Ville de Paris Émergences project “Combinatoire à Paris”.

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Pournin, L. The asymptotic diameter of cyclohedra. Isr. J. Math. 219, 609–635 (2017). https://doi.org/10.1007/s11856-017-1492-0

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  • DOI: https://doi.org/10.1007/s11856-017-1492-0

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