Honam Mathematical Journal (호남수학학술지)

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FACIAL STRUCTURES OF A GENERALIZED WEDGE OF POLYTOPES

  • Kim, Sangwook (Department of Mathematics Chonnam National University)
  • Received : 2016.05.06
  • Accepted : 2016.06.01
  • Published : 2016.06.25
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Abstract

In this paper, we study face and flag information of a generalized wedge of two polytopes over a face. In particular, we provide the explicit formula for the cd-index of the wedge of a polytope and a one-dimensional simplex over an arbitrary face.

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References

  1. Margaret M. Bayer and Andrew Klapper, A new index for polytopes, Discrete Comput. Geom., 6(1) (1991), 33-47. https://doi.org/10.1007/BF02574672
  2. Richard Ehrenborg and Harold Fox, Inequalities for cd-indices of joins and products of polytopes, Combinatorica, 23(3) (2003), 427-452. https://doi.org/10.1007/s00493-003-0026-z
  3. R. Ehrenborg, D. Johnston, R. Rajagopalan, and M. Readdy, Cutting polytopes and ag f-vectors, Discrete Comput. Geom., 23(2) (2000), 261-271. https://doi.org/10.1007/PL00009499
  4. Kerstin Fritzsche and Fred B. Holt, More polytopes meeting the conjectured Hirsch bound, Discrete Math., 205(1-3) (1999), 77-84. https://doi.org/10.1016/S0012-365X(99)00017-5
  5. Bernt Lindstrom, On the realization of convex polytopes, Euler's formula and Mobius functions, Aequationes Math., 6 (1971), 235-240. https://doi.org/10.1007/BF01819757
  6. Andreas Paffenholz, Faces of Birkhoff polytopes, Electron. J. Combin., 22(1) (2015), Paper 1.67, 36.
  7. Thilo Rorig, Polyhedral surfaces, polytopes, and projections. PhD thesis, 2008.
  8. Gian-Carlo Rota, On the combinatorics of the Euler characteristic, In Studies in Pure Mathematics (Presented to Richard Rado), pages 221-233. Academic Press, London, 1971.
  9. Thilo Rorig and Gunter M. Ziegler, Polyhedral surfaces in wedge products, Geom. Dedicata, 151 (2011), 155-173. https://doi.org/10.1007/s10711-010-9524-5
  10. Richard P. Stanley, Enumerative combinatorics. Volume 1. Second edition, volume 49 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2012.