相关论文: Pinned Repetitions in Symbolic Flows: Preliminary …

A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a…

We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…

We afford the problem of counting the blocks of a given length made with symbols drawn from an alphabet and relate this number to Fibonacci-like recurrent relations. The recurrence polynomia allows to calculate the limit ratio of two…

In this paper we discuss a coding and the associated symbolic dynamics for the geodesic flow on Hecke triangle surfaces. We construct an explicit cross section for which the first return map factors through a simple (explicit) map given in…

This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…

In this paper a class of linear maps on the 2-torus and some planar piecewise isometries are discussed. For these discontinuous maps, by introducing codings underlying the map operations, symbolic descriptions of the dynamics and…

We introduce a symbolic representation of $r$-fold harmonic sums at negative indices. This representation allows us to recover and extend some recent results by Duchamp et al., such as recurrence relations and generating functions for these…

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…

This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…

We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.

A recent paper of A. Sofo proves some results about sums of products of quadratic alternating harmonic numbers and reciprocal binomial coefficients. In this paper, we extend his result to cubic alternating harmonic number sums and develop…

Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their…

Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…

Building on the theory of symbolic extensions and uniform generators for discrete transformations we develop a similar theory for topological regular flows. In this context a symbolic extension is given by a suspension flow over a subshift.

This work investigates if the current neural architectures are adequate for learning symbolic rewriting. Two kinds of data sets are proposed for this research -- one based on automated proofs and the other being a synthetic set of…

We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…

We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for…

We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we…

The periodic (ordinal) patterns of a map are the permutations realized by the relative order of the points in its periodic orbits. We give a combinatorial characterization of the periodic patterns of an arbitrary signed shift, in terms of…