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In the paper the notion of {\em Rauzy scheme} is introduced. From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arches. This notion is a tool to describe Rauzy graph behavior.…
We associate to any dynamical system with finitely many periodic orbits of each length a collection of possible time-changes of the sequence of periodic point counts that preserve the property of counting periodic points. Intersecting over…
We naturally obtain some combinatorial identities finding the difference analogs of hyperbolic and trigonometric functions of order $n.$ In particular, we obtain the identities connected with the proved in the paper the addition formulas…
Recurrence quantification analysis is a method for measuring the complexity of dynamical systems. Recurrence determinism is a fundamental characteristic of it, closely related to correlation sum. In this paper, we study asymptotic behavior…
We associate to each synchronous game an algebra whose representations determine if the game has a perfect deterministic strategy, perfect quantum strategy or one of several other perfect strategies. when applied to the graph coloring game,…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
A permutiple is a natural number whose representation in some base, $b>1$, is an integer multiple of a number whose base-$b$ representation has the same collection of digits. Previous efforts have made progress in finding such numbers using…
While there are many identities involving the Euler and Bernoulli numbers, they are usually proved analytically or inductively. We prove two identities involving Euler and Bernoulli numbers with combinatorial reasoning via up-down…
We derive new combinatorial identities which may be viewed as multivariate analogs of summation formulas for hypergeometric series. As in the previous paper [Re], we start with probability distributions on the space of the infinite Young…
The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing…
We characterize unicyclic graphs that are singular using the support of the null space of their pendant trees. From this, we obtain closed formulas for the independence and matching numbers of a unicyclic graph, based on the support of its…
The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.
A new scheme for proving pseudoidentities from a given set {\Sigma} of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when {\Sigma} defines a locally finite variety, a pseudovariety of…
Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit…
Prime numbers appeared in contexts spanning statistical mechanics, quantum mechanics and dynamical systems. However, the mechanisms governing the irregularities observed in their sequence and linking them to physical systems remained…
We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…
We derive several symmetric identities for Bernoulli and Euler polynomials which imply some known identities. Our proofs depend on the new technique developed in part I and some identities obtained in [European J. Combin. 24(2003),…
We describe an algorithm for the sequential sampling of entries in multiway contingency tables with given constraints. The algorithm can be used for computations in exact conditional inference. To justify the algorithm, a theory relates…
The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic,…