An Introduction on Graph Associahedra

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Gürbüzer S. K., Akyar B.

26. Ulusal Matematik Sempozyumu, Diyarbakır, Türkiye, 4 - 07 Eylül 2013

  • Yayın Türü: Bildiri / Yayınlanmadı
  • Basıldığı Şehir: Diyarbakır
  • Basıldığı Ülke: Türkiye
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

By using the algorithm given by Devados [1], we have been worked on the construction

of a graph associahedra, which is a special type of convex polytope. We

have showed that there is an isomorphism between the set of planar trees with

n+1 leaves and the set of compatible tubings on an n-path is given. According

to this isomorphism, the Loday's method and the algorithm given by Devados

is combined to obtain a realization of a graph associahedron. Furthermore, a

fattened tubing on an n 􀀀 1-path is de ned and used for the construction of a

cell structure of an n 􀀀 1 dimensional graph associahedron. Finally, a formula

for the number of simplices in the triangulation of a graph associahedron is

obtained.

2010 AMS Subject Classi cation: 05C10, 52B11, 52B12

Keywords: Graph associahedra, compatible tubing, triangulation, realization.

References

[1] Devados S.L. (2009). A realization of graph associahedra, Discrete Mathematics

Volume 309, Issue 1, Pages 271-276.

[2] Forcey S. and Spring eld D. (2010). Geometric combinatorial algebras: cyclohe-

dron and simplex, J. Algebraic Comb., vol. 32, 597-637, ISSN 0925-9899.

[3] Loday J.L. (2004), Realization of the Stashe polytope, Archiv der Mathematik

83, 267-278.

[4] Loday J.L. (2007), Parking functions and triangulation of the associahedron, Pro-

ceedings of the Street's fest, Contemporary Math. AMS 431, 327-340.