Related papers: Permutation complexity of the fixed points of some…

Let $R(n,k)$ denote the number of permutations of ${1,2,...,n}$ with $k$ alternating runs. In this note we present an explicit formula for the numbers $R(n,k)$.

Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…

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 investigate the asymptotic properties of permutations drawn from the Luce model, a natural probabilistic framework in which permutations are generated sequentially by sampling without replacement, with selection probabilities…

This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…

In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann's theorem on permutations of dense sequences and uniformly distributed sequences of points.

We present an algorithm running in time O(n ln n) which decides if a wreath-closed permutation class Av(B) given by its finite basis B contains a finite number of simple permutations. The method we use is based on an article of Brignall,…

In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number. In this paper, as natural companions to derangement numbers and degenerate…

We define the operation of composing two hereditary classes of permutations using the standard composition of permutations as functions and we explore properties and structure of permutation classes considering this operation. We mostly…

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…

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…

P(n,s) denotes the number of permutations of 1,2,...n that have exactly s sequences. Canfield and Wilf [math.CO/0609704] recently showed that P(n,s) can be written as a sum of s polynomials in n. We determine these polynomials explicitly…

We survey a research program on the strong convergence of unitary and permutation representations of discrete groups. We also take the opportunity to flesh out details that have not appeared elsewhere.

In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.

In this article, we consider the factor complexity of a fixed point of a primitive substitution canonically defined by a beta-numeration system. We provide a necessary and sufficient condition on the Renyi expansion of 1 for having an…

We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a…

We investigate the state complexity of the permutation operation, or the commutative closure, on Alphabetical Pattern Constraints (APC). This class corresponds to level $3/2$ of the Straubing-Th{\'e}rien Hierarchy and includes the finite,…

We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$, in the limit of large $n$. Since in unconstrained uniform random permutations most of the indices are in cycles of…

We compute the degree complexity of a family of birational mappings of the plane with high order singularities.

A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1…