Related papers: Words restricted by patterns with at most 2 distin…
In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern xxx^R was intermediate between polynomial and exponential. We now show that the same holds for the growth of the number of…
We investigate the number of sets of words that can be formed from a finite alphabet, counted by the total length of the words in the set. An explicit expression for the counting sequence is derived from the generating function, and…
In previous papers, for an arithmetical function $f_0$, we defined functions $f_m$ and $c_m$ and designated numbers of restricted words over a finite alphabet counted by these functions. In this paper, we examine the reverse problem for…
We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in…
Following a question of J. Cooper, we study the expected number of occurrences of a given permutation pattern $q$ in permutations that avoid another given pattern $r$. In some cases, we find the pattern that occurs least often, (resp. most…
One major deficiency of most semantic representation techniques is that they usually model a word type as a single point in the semantic space, hence conflating all the meanings that the word can have. Addressing this issue by learning…
The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length <= n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem,…
Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijection is a permutation of the natural numbers…
In this paper we consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by computing closed formulas for the number of trees avoiding a single binary tree pattern with 4 or fewer leaves and compare…
A double occurrence word $w$ over a finite alphabet $\Sigma$ is a word in which each alphabet letter appears exactly twice. Such words arise naturally in the study of topology, graph theory, and combinatorics. Recently, double occurrence…
In this paper, we mainly study two notions of pattern avoidance in parking functions. First, for any collection of length 3 patterns, we compute the number of parking functions of size $n$ that avoid them under the first notion. This is…
Recently, it has been determined that there are 242 Wilf classes of triples of 4-letter permutation patterns by showing that there are 32 non-singleton Wilf classes. Moreover, the generating function for each triple lying in a non-singleton…
In this paper, we complete the enumeration of the number of parking functions of length $n$ avoiding, in the sense defined by Qiu and Remmel, a permutation of length 3, answering several questions of Adeniran and Pudwell. Additionally, we…
This paper is one of a series whose goal is to enumerate the avoiders, in the sense of classical pattern avoidance, for each triple of 4-letter patterns. There are 317 symmetry classes of triples of 4-letter patterns, avoiders of 267 of…
The powerful (and so far under-utilized) Goulden-Jackson Cluster method for finding the generating function for the number of words avoiding, as factors, the members of a prescribed set of `dirty words', is tutorialized and extended in…
Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…
The extension of pattern avoidance from ordinary permutations to those on multisets gave birth to several interesting enumerative results. We study permutations on regular multisets, i.e., multisets in which each element occurs the same…
A Cayley permutation is a word of positive integers such that if a letter appears in this word, then all positive integers smaller than that letter also appear. We initiate a systematic study of pattern avoidance on Cayley permutations…
We consider the language consisting of all words such that it is possible to obtain the empty word by iteratively deleting powers. It turns out that in the case of deleting squares in binary words this language is regular, and in the case…
We construct generating trees with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation,…