Related papers: Counting occurrences of a pattern in a binary word
We consider models for which it is important, early in processing, to estimate some variables with high precision, but perhaps at relatively low rates of recall. If some variables can be identified with near certainty, then they can be…
The joint spectral radius of a bounded set of $d \times d$ real matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. For a fixed set of matrices, a sequence of matrices drawn…
A computational model of the construction of word meaning through exposure to texts is built in order to simulate the effects of co-occurrence values on word semantic similarities, paragraph by paragraph. Semantic similarity is here viewed…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
We present a new semi-external algorithm that builds the Burrows--Wheeler transform variant of Bauer et al. (a.k.a., BCR BWT) in linear expected time. Our method uses compression techniques to reduce computational costs when the input is…
In this paper we consider the following problems: how many different subsets of Sigma^n can occur as set of all length-n factors of a finite word? If a subset is representable, how long a word do we need to represent it? How many such…
The aim of this thesis is to determine classes of NP relations for which random generation and approximate counting problems admit an efficient solution. Since efficient rank implies efficient random generation, we first investigate some…
The Pascal matrix, $P$, is an upper diagonal matrix whose entries are the binomial coefficients. In 1993 Call and Velleman demonstrated that it satisfies the beautiful relation $P=\exp(H)$ in which $H$ has the numbers 1, 2, 3, etc. on its…
Given a word $w$ and a Parikh vector $\mathcal{P}$, an abelian run of period $\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\mathcal{P}$. We give an algorithm that finds all the abelian runs of…
Statistics pedagogy values using a variety of examples. Thanks to text resources on the Web, and since statistical packages have the ability to analyze string data, it is now easy to use language-based examples in a statistics class. Three…
The Binary Two-Up Sequence is the lexicographically earliest sequence of distinct nonnegative integers with the property that the binary expansion of the n-th term has no 1-bits in common with any of the previous floor(n/2) terms. We show…
For $p \in (0,1)$, sample a binary sequence from the infinite product measure of Bernoulli$(p)$ distributions. It is known that for $p=1/2$, almost every binary sequence is Poisson generic in the sense of Peres and Weiss, a property that…
We characterize the words that can be mapped to arbitrarily high powers by injective morphisms. For all other words, we prove a linear upper bound for the highest power that they can be mapped to, and this bound is optimal up to a constant…
Given a pattern $P$ and a text $T$, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of $P$ occurs in $T$. The indexed version of this problem, i.e., preprocessing a…
We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated…
We prove an Erd\H{o}s--Szekeres type result for finite words over $\mathbb{N}$ with repeated values. Specifically, we define a \emph{repeat} in a word to be an occurrence of a value which is not its first occurrence. We define an occurrence…
We discuss the notion of privileged word, recently introduced by Peltomaki. A word w is privileged if it is of length <=1, or has a privileged border that occurs exactly twice in w. We prove the following results: (1) if w^k is privileged…
We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for…
We consider sigma-words, which are words used by Evdokimov in the construction of the sigma-sequence. We then find the number of occurrences of certain patterns and subwords in these words.
These lecture notes provide an introduction to combinatorics on words and its interactions with dynamics, algebra, and arithmetic. The central theme is the notion of low factor complexity for infinite words. We investigate the following…