Related papers: Permutations avoiding bipartite partially ordered …
Let $\mathfrak{O}$ be a compact discrete valuation ring of characteristic zero. Given a module $M$ of matrices over $\mathfrak{O}$, we study the generating function encoding the average sizes of the kernels of the elements of $M$ over…
A partition $\alpha$ is said to contain another partition (or pattern) $\mu$ if the Ferrers board for $\mu$ is attainable from $\alpha$ under removal of rows and columns. We say $\alpha$ avoids $\mu$ if it does not contain $\mu$. In this…
We review selected known results on partially ordered patterns (POPs) that include co-unimodal, multi- and shuffle patterns, peaks and valleys ((modified) maxima and minima) in permutations, the Horse permutations and others. We provide…
In their study of cyclic pattern containment, Domagalski et al. conjecture differential equations for the generating functions of circular permutations avoiding consecutive patterns of length 3. In this note, we prove and significantly…
We present some combinatorial interpretations for coefficients appearing in series partitioning the permutations avoiding 132 along marked mesh patterns. We identify for patterns in which only one parameter is non zero the combinatorial…
In [GM] Guibert and Mansour studied involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern on k letters. They also established a bijection between 132-avoiding…
At the end of the 1960s, Knuth characterised the permutations that can be sorted using a stack in terms of forbidden patterns. He also showed that they are in bijection with Dyck paths and thus counted by the Catalan numbers. Subsequently,…
We study the involutions belonging to the class of 321 avoiding permutations. We calculate the algebraic generating functions of the set containing the involutions avoiding 321 and of some of its subsets. Precisely we determine the…
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
We present a generating function and a closed counting formula in two variables that enumerate a family of classes of permutations that avoid or contain an increasing pattern of length three and have a prescribed number of occurrences of…
In an exercise in the first volume of his famous series of books, Knuth considered sorting permutations by passing them through a stack. Many variations of this exercise have since been considered, including allowing multiple passes through…
This paper introduces the notion of mesh patterns in multidimensional permutations and initiates a systematic study of singleton mesh patterns (SMPs), which are multidimensional mesh patterns of length 1. A pattern is avoidable if there…
We find generating functions for the number of words avoiding certain patterns or sets of patterns on at most 2 distinct letters and determine which of them are equally avoided. We also find the exact number of words avoiding certain…
In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…
We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…
This paper is continuation of the study of the 1-box pattern in permutations introduced by the authors in \cite{kitrem4}. We derive a two-variable generating function for the distribution of this pattern on 132-avoiding permutations, and…
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…
We study the iteration of the process "a particle jumps to the right" in permutations. We prove that the set of permutations obtained in this model after a given number of iterations from the identity is a class of pattern avoiding…
In this paper we continue the study of permutations avoiding the vincular pattern $1-32-4$ by constructing a generating tree with a single label for these permutations. This construction finally provides a clearer explanation of why a…