Related papers: On the Gap sequence and the Gilbreath conjecture
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
The Caccetta-Haggkvist conjecture states that if G is a finite directed graph with at least n/k edges going out of each vertex, then G contains a directed cycle of length at most k. Hamidoune used methods and results from additive number…
In this paper we explore the concept of sequential inductive prediction intervals using theory from sequential testing. We furthermore introduce a 3-parameter PAC definition of prediction intervals that allows us via simulation to achieve…
We relate the notions of spectral gap for unitary representations and subfactors with definability of certain important sets in the corresponding structures. We give several applications of this relationship.
We have developed a notion of global bisimulation distance between processes which goes somehow beyond the notions of bisimulation distance already existing in the literature, mainly based on bisimulation games. Our proposal is based on the…
Lothar Collatz had proposed in 1937 a conjecture in number theory called Collatz conjecture. Till today there is no evidence of proving or disproving the conjecture. In this paper, we propose an algorithmic approach for verification of the…
A method of induction the distances with Hilbert structure is proposed. Some properties of the method are studied. Typical examples of corresponding metric spaces are discussed. Key words: Hilbert spaces; metric spaces; isometric embedding…
Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…
A circular Pascal array is a periodization of the familiar Pascal's triangle. Using simple operators defined on periodic sequences, we find a direct relationship between the ranges of the circular Pascal arrays and numbers of certain…
Let $G$ be a 2-connected graph, $l$ be the length of a longest path in $G$ and $c$ be the circumference - the length of a longest cycle in $G$. In 1952, Dirac proved that $c>\sqrt{2l}$ and conjectured that $c\ge 2\sqrt{l}$. In this paper we…
The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…
Threads as considered in basic thread algebra are primarily looked upon as behaviours exhibited by sequential programs on execution. It is a fact of life that sequential programs are often fragmented. Consequently, fragmented program…
Many aspects of Schubert calculus are easily modeled on a computer. This enables large-scale experimentation to investigate subtle and ill-understood phenomena in the Schubert calculus. A well-known web of conjectures and results in the…
We use generating functions to enumerate Arndt compositions, that is, integer compositions where there is a descent between every second pair of parts, starting with the first and second part, and so on. In 2013, J\"org Arndt noted that…
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.
The classical Three Gap Theorem asserts that for a natural number n and a real number p, there are at most three distinct distances between consecutive elements in the subset of [0,1) consisting of the reductions modulo 1 of the first n…
Motivated by Khintchin's 1923 conjecture, refuted by Marstrand in 1970, we study the Khintchin class of functions associated to a given increasing sequence of integers. When the Khintchin class contains L^p(\mathbb{T}), we call the sequence…
We review several ways of defining the statistics of charge that is transmitted through an electric circuit, the so-called "counting statistics". We first pursue two approaches that explain the origin of "negative probabilities" that have…
We study Aldous' conjecture that the spectral gap of the interchange process on a weighted undirected graph equals the spectral gap of the random walk on this graph. We present a conjecture in the form of an inequality, and prove that this…