Catalan Triangulations of the M Obius
نویسندگان
چکیده
A Catalan triangulation of the MM obius band is an abstract simplicial complex triangulating the MM obius 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 rst 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-ips.
منابع مشابه
Chromatic Statistics for Triangulations and Fuß-Catalan Complexes
We introduce Fuß–Catalan complexes as d-dimensional generalisations of triangulations of a convex polygon. These complexes are used to refine Catalan numbers and Fuß–Catalan numbers, by introducing colour statistics for triangulations and Fuß–Catalan complexes. Our refinements consist in showing that the number of triangulations, respectively of Fuß–Catalan complexes, with a given colour distri...
متن کاملThe Average Number of Non-Separating Edges in Catalan Triangulations of the Mőbius Band and the Cylinder
Let Σ be a surface whose boundary consists of a set of disjoint simple closed curves. A Catalan triangulation of Σ is a triangulation of Σ such that all vertices are on the boundary. An edge in a Catalan triangulation is called separating if the removal of its end vertices disconnects the triangulation. The number of Catalan triangulations of a disk is given by the well-known Catalan numbers. C...
متن کاملTrapezoidal Diagrams, Upward Triangulations, and Prime Catalan Numbers
The d-dimensional Catalan numbers form a well-known sequence of numbers which count balanced bracket expressions over an alphabet of size d. In this paper, we introduce and study what we call d-dimensional prime Catalan numbers, a sequence of numbers which count only a very specific subset of indecomposable balanced bracket expressions. We further introduce the notion of a trapezoidal diagram o...
متن کاملExact uniform sampling over catalan structures
We present a new framework for creating elegant algorithms for exact uniform sampling of important Catalan structures, such as triangulations of convex polygons, Dyck words, monotonic lattice paths and mountain ranges. Along with sampling, we obtain optimal coding, and optimal number of random bits required for the algorithm. The framework is based on an original two-parameter recursive relatio...
متن کاملCounting triangulations and pseudo-triangulations of wheels
Motivated by several open questions on triangulations and pseudotriangulations, we give closed form expressions for the number of triangulations and the number of minimum pseudo-triangulations of n points in wheel configurations, that is, with n − 1 in convex position. Although the numbers of triangulations and pseudotriangulations vary depending on the placement of the interior point, their di...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007