# Permutations defining convex permutominoes.

@article{Bernini2007PermutationsDC, title={Permutations defining convex permutominoes.}, author={Antonio Bernini and Filippo Disanto and Renzo Pinzani and Simone Rinaldi}, journal={Journal of Integer Sequences}, year={2007}, volume={10} }

A permutomino of size n is a polyomino determined by particular pairs (�1,�2) of permutations of size n, such that �1(i) 6 �2(i), for 1 ≤ i ≤ n. Here we determine

## 16 Citations

### On the exhaustive generation of convex permutominoes

- 2008

Mathematics

A permutomino of size n is a polyomino determined by a pair of permutations of size n+1, such that they differ in each position. In this paper, after recalling some enumerative results about…

### Characterization and enumeration of some classes of permutominoes

- 2007

Mathematics

A permutomino of size n is a polyomino whose vertices define a pair of distinct permutations of length n. In this paper we treat various classes of convex permutominoes, including the parallelogram,…

### Polyominoes Determined by Permutations: Enumeration via Bijections

- 2012

Mathematics

A permutominide is a set of cells in the plane satisfying special connectivity constraints and uniquely defined by a pair of permutations. It naturally generalizes the concept of permutomino,…

### Reconstructing convex permutominoes

- 2010

Mathematics

This paper studies the tomographical aspects of a new class of polyominoes, called permutominoes, which are defined by means of a pair of permutations. We inspect the classical problems of uniqueness…

### On the enumeration of column-convex permutominoes

- 2011

Mathematics

We study the enumeration of \emphcolumn-convex permutominoes, i.e. column-convex polyominoes defined by a pair of permutations. We provide a direct recursive construction for the column-convex…

### A code for square permutations and convex permutominoes

- 2019

Mathematics

Discret. Math. Theor. Comput. Sci.

In this article we consider square permutations, a natural subclass of permutations defined in terms of geometric conditions, that can also be described in terms of pattern avoiding permutations, and…

### Polyominoes determined by involutions

- 2008

Mathematics

A permutomino of size n is a polyomino determined by particular pairs (π 1 , π 2 ) of permutations of length n , such that π 1 (i)≠π 2 (i) , for 1≤i≤n . In this paper we consider the class of convex…

### About Half Permutations

- 2014

Mathematics

Electron. J. Comb.

The class of $dcc$-permutations is a new class of permutations counted by half factorial numbers, and here it is shown some combinatorial characterizations of this class, using the concept of logical formulas determined by a permutation and the notion of mesh pattern.

### Square Involutions

- 2011

Mathematics

A square involution is a square permutation which is also an involution. In this paper we give the enumeration of square involutions, using purely combinatorial methods, by establishing a bijective…

## 26 References

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Mathematics

In this paper we consider the class of $\textit{permutominoes}$, i.e. a special class of polyominoes which are determined by a pair of permutations having the same size. We give a characterization of…

### A Closed Formula for the Number of Convex Permutominoes

- 2007

Mathematics

Electron. J. Comb.

A closed formula is determined for the number of convex permutominoes of size $n+1$ by providing a recursive generation of all convex permits of size n from the objects of sizen, according to the ECO method, and translating this construction into a system of functional equations satisfied by the generating function of conveX permutOMinoes.

### Counting Polyominoes on Twisted Cylinders

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Mathematics

We improve the lower bounds on Klarner's constant, which describes the exponential growth rate of the number of polyominoes (connected subsets of grid squares) with a given number of squares. We…

### Permutation Diagrams, Fixed Points and Kazhdan-Lusztig R-Polynomials

- 2006

Mathematics

Abstract.In this paper, we give an algorithm for computing the Kazhdan-Lusztig R-polynomials in the symmetric group. The algorithm is described in terms of permutation diagrams. In particular we…

### A Note on a Result of Daurat and Nivat

- 2005

Mathematics

Developments in Language Theory

A characteristic property of self-avoiding closed paths is obtained, generalizing in this way a recent result of Daurat and Nivat on the boundary properties of polyominoes concerning salient and reentrant points.

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- 2007

Mathematics, Computer Science

This work defines an injective map between permutations of length n and a subset of grid polygons on n vertices, which they are called consecutive-minima polygons, and enumerates sets of permutations whose consecutive- Minima polygon satisfy specific geometric conditions by the kernel method.

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Mathematics

A self-avoiding polygon (SAP) on a graph is an elementary cycle. Counting SAPs on the hypercubic lattice ℤd withd≥2, is a well-known unsolved problem, which is studied both for its combinatorial and…