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Catalan Triangulations of the Möbius Band

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Abstract

A Catalan triangulation of the Möbius band is an abstract simplicial complex triangulating the Möbius band which uses no interior vertices, and has vertices labelled 1, 2, …, n in order as one traverses the boundary. We prove two results about the structure of this set, analogous to well-known results for Catalan triangulations of the disk. The first is a generating function for Catalan triangulations of M having n vertices, and the second is that any two such triangulations are connected by a sequence of diagonal-flips.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Paul H. Edelman & Victor Reiner

Authors
  1. Paul H. Edelman
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  2. Victor Reiner
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Corresponding author

Correspondence to Paul H. Edelman.

Additional information

Work of Edelman and Reiner partially supported by NSF grant DMS-9201490, and Mathematical Sciences Postdoctoral Research Fellowship DMS-9206371, respectively

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Edelman, P.H., Reiner, V. Catalan Triangulations of the Möbius Band. Graphs and Combinatorics 13, 231–243 (1997). https://doi.org/10.1007/BF03353000

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  • DOI: https://doi.org/10.1007/BF03353000

1991 Mathematics Subject Classification