Diagonally convex directed polyominoes and even trees: a bijection and related issues

  • Authors:
  • Emeric Deutsch;Svjetlan Feretic;Marc Noy

  • Affiliations:
  • Department of Mathematics, Polytechnic University, Brooklyn, NY;Setaliste Joakima Rakovca 17, 51000 Rijeka, Croatia;Department of Applied Mathematics, Universitat Politecnica de Catalunya, Pau Gargallo, 5, 08028 Barcelona, Spain

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2002

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Abstract

We present a simple bijection between diagonally convex directed (DCD) polyominoes with n diagonals and plane trees with 2n edges in which every vertex has even degree (even trees), which specializes to a bijection between parallelogram polyominoes and full binary trees. Next we consider a natural definition of symmetry for DCD-polyominoes, even trees, ternary trees, and non-crossing trees, and show that the number of symmetric objects of a given size is the same in all four cases.