Related papers: A survey of consecutive patterns in permutations
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
We initiate a general approach for the fast enumeration of permutations with a prescribed number of occurrences of `forbidden' patterns, that seems to indicate that the enumerating sequence is always P-recursive. We illustrate the method…
An alternating permutation of length $n$ is a permutation $\pi=\pi_1 \pi_2 ... \pi_n$ such that $\pi_1 < \pi_2 > \pi_3 < \pi_4 > ...$. Let $A_n$ denote set of alternating permutations of ${1,2,..., n}$, and let $A_n(\sigma)$ be set of…
We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…
In this paper, we propose a general framework that extends the theory of permutation patterns to higher dimensions and unifies several combinatorial objects studied in the literature. Our approach involves introducing the concept of a…
We consider a class of real numbers, a subset of irrational numbers and certain mathematical constants, for which the elements in the simple continued fraction appears to be random. As an illustrative example, one can consider $\pi = \{x_0,…
Motivated by a problem in quantum field theory, we study the up and down structure of circular and linear permutations. In particular, we count the length of the (alternating) runs of permutations by representing them as monomials and find…
We present a new approach to the problem of enumerating permutations of length n that avoid a fixed consecutive pattern of length m. We use this idea to give explicit upper and lower bounds on the number of permutations avoiding a pattern…
The periodic (ordinal) patterns of a map are the permutations realized by the relative order of the points in its periodic orbits. We give a combinatorial characterization of the periodic patterns of an arbitrary signed shift, in terms of…
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called feasible region. We show that this feasible region is a…
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the limit of such proportions on large permutations forms a region, called \emph{feasible region}. We show that this feasible region is a…
Shuffle algebras are monoids for an unconvential monoidal category structure on graded vector spaces. We present two homological results on shuffle algebras with monomial relations, and use them to prove exact and asymptotic results on…
In the last years, different types of patterns in permutations have been studied: vincular, bivincular and mesh patterns, just to name a few. Every type of permutation pattern naturally defines a corresponding computational problem: Given a…
We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…
The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
Pin sequences play an important role in the structural study of permutation classes. In this paper, we study the permutation classes that comprise all the finite subpermutations contained in an infinite pin sequence. We prove that these…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…
Permutations that avoid given patterns have been studied in great depth for their connections to other fields of mathematics, computer science, and biology. From a combinatorial perspective, permutation patterns have served as a unifying…