Related papers: Random and exhaustive generation of permutations a…
A universal cycle for permutations of length $n$ is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length $n$, and containing all permutations of length $n$ as factors. It is well known…
In order to study how well a finite group might be generated by repeated random multiplications, P. Diaconis suggested the following urn model. An urn contains some balls labeled by elements which generate a group G. Two are drawn at random…
Using the recently developed notion of permutation limits this paper derives the limiting distribution of the number of fixed points and cycle structure for any convergent sequence of random permutations, under mild regularity conditions.…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
For uniform random permutations conditioned to have no long cycles, we prove that the total number of cycles satisfies a central limit theorem. Under additional assumptions on the asymptotic behavior of the set of allowed cycle lengths, we…
Efficient algorithms for searching for optimal saturated designs are widely available. They maximize a given efficiency measure (such as D-optimality) and provide an optimum design. Nevertheless, they do not guarantee a \emph{global}…
This article presents a methodology that automatically derives a combinatorial specification for a permutation class C, given its basis B of excluded patterns and the set of simple permutations in C, when these sets are both finite. This is…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent years. In this survey article we discuss some of the…
Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov…
We look at geometric limits of large random non-uniform permutations. We mainly consider two theories for limits of permutations: permuton limits, introduced by Hoppen, Kohayakawa, Moreira, Rath, and Sampaio to define a notion of scaling…
We describe the limit (for two topologies) of large uniform random square permutations, i.e., permutations where every point is a record. The starting point for all our results is a sampling procedure for asymptotically uniform square…
We give a generating function for the number of unimodal permutations with a given cycle structure.
The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
We first fully implement, in Maple, the ingenious method of Robert Stoyan and Volker Strehl from 1995 to automatically derive generating functions for the number of Hamiltonian cycles in an m by n grid graph ,for a fixed width m, but…
Random sampling is a technique for signal acquisition which is gaining popularity in practical signal processing systems. Nowadays, event-driven analog-to-digital converters make random sampling feasible in practical applications. A process…
Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…
Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically…
In this work we obtain recurrent formulae for the number of permutations with either increasing or monotonic (i.e., both increasing and decreasing) runs of bounded length. Our formulae allow one to efficiently compute the number of such…