Vincent Pilaud ; Francisco Santos - Multi-triangulations as complexes of star polygons

dmtcs:3642 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3642
Multi-triangulations as complexes of star polygons

Authors: Vincent Pilaud ORCID-iD1; Francisco Santos ORCID-iD2

A $k$-triangulation of a convex polygon is a maximal set of diagonals so that no $k+1$ of them mutually cross. $k$-triangulations have received attention in recent literature, with motivation coming from several interpretations of them. We present a new way of looking at $k$-triangulations, where certain star polygons naturally generalize triangles for $k$-triangulations. With this tool we give new, direct proofs of the fundamental properties of $k$-triangulations (number of edges, definition of flip). This interpretation also opens up new avenues of research that we briefly explore in the last section.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: generalized triangulation,crossing-free graph,star polygon,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV 1009.4690
Source : ScholeXplorer IsRelatedTo DOI 10.37236/1167
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1009.4690
  • 1009.4690
  • 10.48550/arxiv.1009.4690
  • 10.37236/1167
  • 10.37236/1167
Maximal Fillings of Moon Polyominoes, Simplicial Complexes, and Schubert Polynomials

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