Related papers: Combinatorial generation via permutation languages…
We first show that the tilings of a general domain form a lattice which we then undertake to decompose and generate without any redundance. To this end, we study extensively the relatively simple case of hexagons and their deformations. We…
In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
The conference GASCom brings together researchers in combinatorics, algorithms, probabilities, and more generally mathematical computer science, around the theme of random and exhaustive generation of combinatorial structures, mostly…
A random planar quadrangulation process is introduced as an approximation for certain cellular automata in terms of random growth of rays from a given set of points. This model turns out to be a particular (rectangular) case of the…
We consider random instances of non-convex perceptron problems in the high-dimensional limit of a large number of examples $M$ and weights $N$, with finite load $\alpha = M/N$. We develop a formalism based on replica theory to predict the…
We propose a unified approach for bottom-up hierarchical image segmentation and object proposal generation for recognition, called Multiscale Combinatorial Grouping (MCG). For this purpose, we first develop a fast normalized cuts algorithm.…
Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules.…
With sound unification, Definite Clause Grammars and compact expression of combinatorial generation algorithms, logic programming is shown to conveniently host a declarative playground where interesting properties and behaviors emerge from…
We study aspects of the enumeration of permutation classes, sets of permutations closed downwards under the subpermutation order. First, we consider monotone grid classes of permutations. We present procedures for calculating the generating…
For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for…
The theory of spin models intersects with condensed matter physics, complex systems, graph theory, combinatorial optimization, computational complexity and neural networks. Many ensuing applications rely on the fact that complicated spin…
We develop a nonstandard approach to exploring polynomials associated with peaks and runs of permutations. With the aid of a context-free grammar, or a set of substitution rules, one can perform a symbolic calculus, and the computation…
Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…
In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the…
A \emph{generic rectangular layout} (for short, \emph{layout}) is a subdivision of an axis-aligned rectangle into axis-aligned rectangles, no four of which have a point in common. Such layouts are used in data visualization and in…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the…