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.
Original language | English (US) |
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Pages (from-to) | 231-243 |
Number of pages | 13 |
Journal | Graphs and Combinatorics |
Volume | 13 |
Issue number | 3 |
DOIs | |
State | Published - Jan 1 1997 |