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Cesar Ceballos ; Arnau Padrol ; Camilo Sarmiento - Dyck path triangulations and extendability (extended abstract)

dmtcs:2516 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2516
Dyck path triangulations and extendability (extended abstract)Conference paper

Authors: Cesar Ceballos 1; Arnau Padrol 2; Camilo Sarmiento 3

  • 1 Department of Mathematics and Statistics [Toronto]
  • 2 Institut für Mathematik
  • 3 Institut fuer Algebra und Geometrie, Magdeburg

We introduce the Dyck path triangulation of the cartesian product of two simplices Δn1×Δn1. The maximal simplices of this triangulation are given by Dyck paths, and its construction naturally generalizes to produce triangulations of Δr n1×Δn1 using rational Dyck paths. Our study of the Dyck path triangulation is motivated by extendability problems of partial triangulations of products of two simplices. We show that whenevermk>n, any triangulations of Δ(k1)m1×Δn1 extends to a unique triangulation of Δm1×Δn1. Moreover, with an explicit construction, we prove that the bound k>n is optimal. We also exhibit interpretations of our results in the language of tropical oriented matroids, which are analogous to classical results in oriented matroid theory.


Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: triangulations,products of simplices,Dyck paths,tropical oriented matroids,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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