Related papers: Pattern Avoiding Ballot Paths and Finite Operator …
In recent years, there has been increasing interest in consecutive pattern avoidance in permutations. In this paper, we introduce two approaches to counting permutations that avoid a set of prescribed patterns consecutively. These algoritms…
The evaluation mechanism of pattern matching with dynamic patterns is modelled in the Pure Pattern Calculus by one single meta-rule. This contribution presents a refinement which narrows the gap between the abstract calculus and its…
This paper considers the enumeration of ternary trees (i.e. rooted ordered trees in which each vertex has 0 or 3 children) avoiding a contiguous ternary tree pattern. We begin by finding recurrence relations for several simple tree…
In this paper we study the enumeration and the construction, according to the number of ones, of particular binary words avoiding a fixed pattern. The growth of such words can be described by particular jumping and marked succession rules.…
The number of inversion sequences avoiding two patterns $101$ and $102$ is known to be the same as the number of permutations avoiding three patterns $2341$, $2431$, and $3241$. This sequence also counts the number of Schr\"{o}der paths…
We consider the enumeration of pattern-avoiding involutions, focusing in particular on sets defined by avoiding a single pattern of length 4. As we demonstrate, the numerical data for these problems demonstrates some surprising behavior.…
A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…
There are several versions of permutation pattern avoidance that have arisen in the literature, and some known examples of two different types of pattern avoidance coinciding. In this paper, we examine barred patterns and vincular patterns.…
This paper presents a collection of experimental results regarding permutation pattern avoidance, focusing on cases where there are "many" patterns to be avoided.
In this paper, the problem of pattern avoidance in generalized non-crossing trees is studied. The generating functions for generalized non-crossing trees avoiding patterns of length one and two are obtained. Lagrange inversion formula is…
In this paper, we consider several combinatorial problems whose enumeration leads to the odd-indexed Fibonacci numbers, including certain types of Dyck paths, block fountains, directed column-convex polyominoes, and set partitions with no…
Within the context of the binomial model, we analyse sequences of values that are almost-uniform and we discuss a prediction method called the frequent outcome approach, in which the outcome that has occurred the most in the observed trials…
We study pattern avoidance by combinatorial objects other than permutations, namely by ordered partitions of an integer and by permutations of a multiset. In the former case we determine the generating function explicitly, for integer…
Given a set $\Pi$ of permutation patterns of length at most $k$, we present an algorithm for building $S_{\le n}(\Pi)$, the set of permutations of length at most $n$ avoiding the patterns in $\Pi$, in time $O(|S_{\le n - 1}(\Pi)| \cdot k +…
In this paper, we propose to consider various models of pattern recognition. At the same time, it is proposed to consider models in the form of two operators: a recognizing operator and a decision rule. Algebraic operations are introduced…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
We investigate pattern avoidance in permutations satisfying some additional restrictions. These are naturally considered in terms of avoiding patterns in linear extensions of certain forest-like partially ordered sets, which we call binary…
Range Avoidance (AVOID) is a total search problem where, given a Boolean circuit $C\colon\{0,1\}^n\to\{0,1\}^m$, $m>n$, the task is to find a $y\in\{0,1\}^m$ outside the range of $C$. For an integer $k\geq 2$, $\mathrm{NC}^0_k$-AVOID is a…
We enumerate and characterize some classes of alternating and reverse alternating involutions avoiding a single pattern of length three or four. If on one hand the case of patterns of length three is trivial, on the other hand, the length…
Patience Sorting is a combinatorial algorithm that can be viewed as an iterated, non-recursive form of the Schensted Insertion Algorithm. In recent work the authors have shown that Patience Sorting provides an algorithmic description for…