## 7 Citations

### Counting Quiddities of Polygon Dissections

- MathematicsThe Mathematical Intelligencer
- 2022

A dissection is a partition of a convex polygon into sub-polygons, or cells, by non-crossing diagonals. The simplest and most popular class of dissections is the triangulations, where the cells are…

### The Central Component of a Triangulation

- Mathematics
- 2013

We define the central component of a triangulation of a regular convex polygon as the diameter or triangle containing its geometric center. This definition yields a new recursion relation for Catalan…

### Decompositions of a Polygon into Centrally Symmetric Pieces

- Mathematics
- 2015

In this paper we deal with edge-to-edge, irreducible decompositions of a centrally symmetric convex (2k)-gon into centrally symmetric convex pieces. We prove an upper bound on the number of these…

### Decompositions of a Polygon into Centrally Symmetric Pieces

- MathematicsMediterranean Journal of Mathematics
- 2016

In this paper we deal with edge-to-edge, irreducible decompositions of a centrally symmetric convex (2k)-gon into centrally symmetric convex pieces. We prove an upper bound on the number of these…

### The S n +1 Action on Spherical Models and Supermaximal Models of Tipe A n −1

- Mathematics
- 2015

In this paper we recall the construction of the De Concini–Procesi wonderful models of the braid arrangement: these models, in the case of the braid arrangement of type An−1, are equipped with a…

### Recurrent Neural Networks as Optimal Mesh Refinement Strategies

- Computer ScienceComput. Math. Appl.
- 2021

### Number of Dissections of the Regular n-gon by Diagonals

- MathematicsJ. Integer Seq.
- 2017

This paper presents a formula for the distinct dissections by diagonals of a regular n-gon modulo the action of the dihedral group, utilizing a corollary of the CauchyFrobenius theorem, which involves counting of cycles.

## References

SHOWING 1-10 OF 18 REFERENCES

### Counting equivalence classes of vertex pairs modulo the dihedral action on the associahedron

- Mathematics
- 2012

This paper proves explicit formulae for the number of edges, 2-sets and diagonals in the associahedron of dimension n modulo the action of the dihedral group. A generating function for the number of…

### Polygon Dissections and Euler, Fuss, Kirkman, and Cayley Numbers

- MathematicsJ. Comb. Theory, Ser. A
- 2000

A short and elementary proof of the formulas for classical numbers of polygon dissections is given and the relationship between the proof, recent work in knot theory, and Jones' work on planar algebras is described.

### Closed Forms for the Number of Polygon Dissections

- MathematicsJ. Symb. Comput.
- 1995

It is proved that if the parameter r is fixed then the number of dissections is quasi-polymonial in s, and it is proposed that unlabelled dissections of the regular s-gon into r cells by means of nonintersecting diagonals are considered.

### Cellular Structures Determined by Polygons and Trees

- Mathematics
- 2000

Abstract. The polytope structure of the associahedron is decomposed into two categories, types and classes. The classification of types is related to integer partitions, whereas the classes present a…

### Triangular Dissections of N-Gons

- MathematicsCanadian Mathematical Bulletin
- 1963

Let f(n) denote the number of dissections of a regular n-gon into n-2 triangles by n-3 non-intersecting diagonals. It is known that and that 1 for n = 3, 4, . . . , where f(2) = 1 by definition. (For…

### COUNTING CLUSTER-TILTED ALGEBRAS OF TYPE An

- Mathematics
- 2008

The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type An, by counting the mutation class of any quiver with underlying graph An. It…

### Triangulations: Structures for Algorithms and Applications

- Mathematics
- 2010

Triangulations appear everywhere, from volume computations and meshing to algebra and topology. This book studies the subdivisions and triangulations of polyhedral regions and point sets and presents…

### Theory of Groups of Finite Order

- MathematicsNature
- 1911

IN the new edition of Prof. Burnside's standard work important changes have been made by rearrangement of old material, and by addition of new. The main feature, for which many English readers will…