Related papers: Passing through a stack $k$ times

In this article, we describe an algorithm to determine whether a permutation class C given by a finite basis B of excluded patterns contains a finite number of simple permutations. This is a continuation of the work initiated in [Brignall,…

We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are…

For each positive integer $k$, we consider five well-studied posets defined on the set of Dyck paths of semilength $k$. We prove that uniquely sorted permutations avoiding various patterns are equinumerous with intervals in these posets.…

Let T_k^m={\sigma \in S_k | \sigma_1=m}. We prove that the number of permutations which avoid all patterns in T_k^m equals (k-2)!(k-1)^{n+1-k} for k <= n. We then prove that for any \tau in T_k^1 (or any \tau in T_k^k), the number of…

The pop-stack-sorting process is a variation of the stack-sort process. We consider a deterministic version of this process, and provide a new lower bound of $\frac{3}{5}n$ for the number of sorts to fully sort a uniformly randomly chosen…

Dokos et. al. studied the distribution of two statistics over permutations $\mathfrak{S}_n$ of $\{1,2,\dots, n\}$ that avoid one or more length three patterns. A permutation $\sigma\in\mathfrak{S}_n$ contains a pattern…

We construct a refined bijection $\phi$ between alternating permutations and 0-1-2 increasing trees with degree at most 2. It satisfies that the first element of alternating permutation $\pi$ is equal to the first vertex in $\phi(\pi)$ in…

In the first paper in this series we estimated the probability that a random permutation $\pi\in\mathcal{S}_n$ has a fixed set of a given size. In this paper, we elaborate on the same method to estimate the probability that $\pi$ has $m$…

The subject of pattern avoiding permutations has its roots in computer science, namely in the problem of sorting a permutation through a stack. A formula for the number of permutations of length n that can be sorted by passing it twice…

This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…

An infinite permutation is a linear ordering of the set of natural numbers. An infinite permutation can be defined by a sequence of real numbers where only the order of elements is taken into account. In the paper we investigate a new class…

The technique of in-situ associative permuting is introduced which is an association of in-situ permuting and in-situ inverting. It is suitable for associatively permutable permutations of {1,2,...,n} where the elements that will be…

Pin permutations play an important role in the structural study of permutation classes, most notably in relation to simple permutations and well-quasi-ordering, and in enumerative consequences arising from these. In this paper, we continue…

A permutation of n letters is k-prolific if each (n-k)-subset of the letters in its one-line notation forms a unique pattern. We present a complete characterization of k-prolific permutations for each k, proving that k-prolific permutations…

We prove that the set of permutations generated by a stack of depth two and an infinite stack in series has a basis (defining set of forbidden patterns) consisting of 20 permutations of length 5, 6, 7 and 8. We prove this via a…

Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…

In this work of thesis we introduce and study a new family of sorting devices, which we call pattern-avoiding machines. They consist of two stacks in series, equipped with a greedy procedure. On both stacks we impose a static constraint in…

A $k$-universal permutation, or $k$-superpermutation, is a permutation that contains all permutations of length $k$ as patterns. The problem of finding the minimum length of a $k$-superpermutation has recently received significant attention…

We define two new statistics on words: the k-connector and the gk-connector. For a word $\pi = \pi_1\pi_2\cdots\pi_n$ of length $n$ over the alphabet $[k]$, a k-connector is defined as an ordered pair $(\pi_j, \pi_{j+1})$ where $1 \leq j…

Permutations in the image of the pop-stack operator are said to be pop-stacked. We give a polynomial-time algorithm to count pop-stacked permutations up to a fixed length and we use it to compute the first 1000 terms of the corresponding…