Related papers: Central sets defined by words of low factor comple…
An infinite permutation is a linear ordering of the set of natural numbers. An infinite permutation can be defined by a sequence of real numbers where only the order of elements is taken into account. In the paper we investigate a new class…
We explain how to see finite combinatorics of preorders implicit in the {text} of basic topological definitions or arguments in (Bourbaki, General topology, Ch.I), and define a concise combinatorial notation such that complete definitions…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
The Central sets theorem was first introduced by H. Furstenberg [F] in terms of Dynamical systems. Later Hindman and Bergelson extended the theorem using Stone-$\v{C}$ech compactification $\beta$$\mathbb{N}$ of $\mathbb{N}$. In [SY]…
Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate…
We study models of HST, a nonstandard set theory which includes, in particular, the ZFC Replacement and Separation schemata in the language containing the membership and standardness predicates, and Saturation for well-orderable families of…
Seriation methods order a set of descriptions given some criterion (e.g., unimodality or minimum distance between similarity scores). Seriation is thus inherently a problem of finding the optimal solution among a set of permutations of…
We consider a component of the word statistics known as clump; starting from a finite set of words, clumps are maximal overlapping sets of these occurrences. This parameter has first been studied by Schbath with the aim of counting the…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
ZFC has sentences that quantify over all sets or all ordinals, without restriction. Some have argued that sentences of this kind lack a determinate meaning. We propose a set theory called TOPS, using Natural Deduction, that avoids this…
A coreset (or core-set) of an input set is its small summation, such that solving a problem on the coreset as its input, provably yields the same result as solving the same problem on the original (full) set, for a given family of problems…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…
Central, standard, and Christoffel words are three strongly interrelated classes of binary finite words which represent a finite counterpart of characteristic Sturmian words. A natural arithmetization of the theory is obtained by…
A proper infinite parallelepiped (IP) set in a semigroup is an infinite set consisting of a sequence $\myseq{a}$ and its finite sums, or a superset of such a set. Hindman's theorem asserts that the proper IP sets of natural numbers are…
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
In their proof of the IP Szemer\'edi theorem, a far reaching extension of the classic theorem of Szemer\'edi on arithmetic progressions, Furstenberg and Katznelson introduced an important class of additively large sets called…
We define a generic algorithmic framework to prove pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substitutions. We focus on the families obtained as finite products of…
Topic models are a useful analysis tool to uncover the underlying themes within document collections. The dominant approach is to use probabilistic topic models that posit a generative story, but in this paper we propose an alternative way…
In [2], while studying a relevant class of polyominoes that tile the plane by translation, i.e., double square polyominoes, the authors found that their boundary words, encoded by the Freeman chain coding on a four letters alphabet, have…
We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence…