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We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either…
We describe a very simple method for `consistent sampling' that allows for sampling with replacement. The method extends previous approaches to consistent sampling, which assign a pseudorandom real number to each element, and sample those…
The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations.
The paperfolding sequences form an uncountable class of infinite sequences over the alphabet $\{ -1, 1 \}$ that describe the sequence of folds arising from iterated folding of a piece of paper, followed by unfolding. In this note we observe…
The length $\mathsf{is}(\pi)$ of a longest increasing subsequence in a permutation $\pi$ has been extensively studied. An increasing subsequence is one that has no descents. We study generalizations of this statistic by finding longest…
A numerical semigroup is an additive subsemigroup of the natural numbers that contains zero and has finite complement. A numerical semigroup is irreducible if it cannot be written as an intersection of numerical semigroups properly…
Superlatives are used to single out elements with a maximal/minimal property. Semantically, superlatives perform a set comparison: something (or some things) has the min/max property out of a set. As such, superlatives provide an ideal…
We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…
The subword complexity of a finite word $w$ of length $N$ is a function which associates to each $n\le N$ the number of all distinct subwords of $w$ having the length $n$. We define the \emph{maximal complexity} C(w) as the maximum of the…
A permutation $\sigma \in S_n$ is a $k$-superpattern (or $k$-universal) if it contains each $\tau \in S_k$ as a pattern. This notion of "superpatterns" can be generalized to words on smaller alphabets, and several questions about…
We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
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…
Universal outlier hypothesis testing is studied in a sequential setting. Multiple observation sequences are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are…
A permutiple is the product of a digit preserving multiplication, that is, a number which is an integer multiple of some permutation of its digits. Certain permutiple problems, particularly transposable, cyclic, and, more recently,…
The dominant approach to sequence generation is to produce a sequence in some predefined order, e.g. left to right. In contrast, we propose a more general model that can generate the output sequence by inserting tokens in any arbitrary…
We introduce the notion of a Morse sequence, which provides a simple and effective approach to discrete Morse theory. A Morse sequence is a sequence composed solely of two elementary operations, that is, expansions (the inverse of a…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
We prove that, for every decreasing sequence {a \sb k} of natural numbers, there exists a map f: X --> X with cat (f\sp k)=a\sb k.