Multi - pseudotriangulations

نویسندگان

  • Vincent Pilaud
  • Michel Pocchiola
چکیده

We introduce a natural generalization of both pseudotriangulations and multitriangulations, that we call multi-pseudotriangulations. We propose an enumeration algorithm for multi-pseudotriangulations, based on certain greedy multi-pseudotriangulations that are closely related with sorting networks. The proofs of the results of this extended abstract are skipped for space reasons.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Multitriangulations, pseudotriangulations and primitive sorting networks

We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration algorithm for arrangements with a given support, based on the properties of certain greedy pseudoline arrangements and on their connection with sorting networks....

متن کامل

Counting 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 کامل

Catalan numbers, binary trees, and pointed pseudotriangulations

We study connections among structures in commutative algebra, combinatorics, and discrete geometry, introducing an array of numbers, called Borel’s triangle, that arises in counting objects in each area. By defining natural combinatorial bijections between the sets, we prove that Borel’s triangle counts the Betti numbers of certain Borel-fixed ideals, the number of binary trees on a fixed numbe...

متن کامل

A pointed Delaunay pseudo-triangulation of a simple polygon

We present a definition of a pointed Delaunay pseudotriangulation of a simple polygon. We discuss why our definition is reasonable. Our approach will be motivated from maximal locally convex functions, and extends the work of Aichholzer et al.[1]. Connections between the polytope of the pointed pseudotriangulations and the Delaunay pseudo-triangulation will be given.

متن کامل

Cluster Algebras of Type D: Pseudotriangulations Approach

We present a combinatorial model for cluster algebras of type Dn in terms of centrally symmetric pseudotriangulations of a regular 2n-gon with a small disk in the centre. This model provides convenient and uniform interpretations for clusters, cluster variables and their exchange relations, as well as for quivers and their mutations. We also present a new combinatorial interpretation of cluster...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009