Blog
About

11
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Non-crossing chords of a polygon with forbidden positions

      Preprint

      , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          In this paper we investigate non-crossing chords of simple polygons in the plane systematically. We first develop the Euler characteristic of a family of line-segments, and subsequently study the structure of the diagonals and epigonals of a polygon. A special phenomenon is that the Euler characteristic of a set of diagonals (or epigonals) characterizes the geometric property of polygons, such as convexity. In particular, a positive answer is given to an open problem proposed by Shephard. The main contributions of the present paper extend such research to non-crossing diagonals and epigonals with forbidden positions. We find that the Euler characteristic of diagonals (or epigonals) with forbidden positions determine the types of polygon in surprising ways. Incidentally, some kinds of generalized Catalan's number naturally arise.

          Related collections

          Most cited references 4

          • Record: found
          • Abstract: not found
          • Article: not found

          The Associahedron and Triangulations of the n-gon

           Carl W Lee (1989)
            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Polygon Dissections and Euler, Fuss, Kirkman, and Cayley Numbers

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Divided differences of inverse functions and partitions of a convex polygon

                Bookmark

                Author and article information

                Journal
                2016-11-09
                Article
                1611.03166

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                51E12, 05B25, 51D20, 51E30
                19 pages
                math.CO

                Combinatorics

                Comments

                Comment on this article