Related papers: Characterizing Follower and Extender Set Sequences
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
We study here a sequence of secondary measures, so called because the set of secondary polynomials on a given term become orthogonal for the next measure. The main result is a formula making explicit the density of any term of the sequence,…
To render a sequence testable, namely capable of identifying and detecting errors, it is necessary to apply a transformation that increases its length by introducing statistical dependence among symbols, as commonly exemplified by the…
We show that the set of realizations of a given dimension of a max-plus linear sequence is a finite union of polyhedral sets, which can be computed from any realization of the sequence. This yields an (expensive) algorithm to solve the…
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the limit of such proportions on large permutations forms a region, called \emph{feasible region}. We show that this feasible region is a…
A topological group $X$ is called connected if the only subsets which are both open and closed are the whole space $X$ and the null set $\emptyset$. A subset of a topological group is connected if the subspace is connected. We say that a…
A sequence x=x_1 x_2...x_n $ is said to be an ascent sequence of length $n$ if it satisfies x_1=0 and $0\leq x_i\leq asc(x_1x_2...x_{i-1})+1$ for all $2\leq i\leq n$, where $asc(x_1x_2... x_{i-1})$ is the number of ascents in the sequence…
By replacing the letters to polynomials in F_2[t], an infinite word, over a finite alphabet, can be seen as the sequence of partial quotients of a continued fraction in F_2((1/t)). Here is described a family of such infinite words,…
A tree $T$ on $2^n$ vertices is called set-sequential if the elements in $V(T)\cup E(T)$ can be labeled with distinct nonzero $(n+1)$-dimensional $01$-vectors such that the vector labeling each edge is the component-wise sum modulo $2$ of…
We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field $\mathbb{F}$. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words,…
We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it…
We explore a family of nested recurrence relations with arbitrary levels of nesting, which have an interpretation in terms of fixed points of morphisms over a countably infinite alphabet. Recurrences in this family are related to a number…
Let $\beta\in(1,2)$ and $x\in [0,\frac{1}{\beta-1}]$. We call a sequence $(\epsilon_{i})_{i=1}^\infty\in\{0,1\}^{\mathbb{N}}$ a $\beta$-expansion for $x$ if $x=\sum_{i=1}^{\infty}\epsilon_{i}\beta^{-i}$. We call a finite sequence…
A collection of complex sequences of length v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequence A=[a_0,a_1,...,a_{v-1}] of length v=dm we define the…
There exists a particular subset of algebraic power series over a finite field which, for different reasons, can be compared to the subset of quadratic real numbers. The continued fraction expansion for these elements, called…
The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher dimensional analogues of continued…
Infinite sequences are of tremendous theoretical and practical importance, and in the Information Age sequences of 0s and 1s are of particular interest. Over the past century, the field of symbolic dynamics has developed to study sequences…
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…
Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…