Related papers: On the geometry behind a recurrent relation
We introduce the chain geometry $\Sigma(K,R)$ over a ring $R$ with a distinguished subfield $K$, thus extending the usual concept where $R$ has to be an algebra over $K$. A chain is uniquely determined by three of its points, if, and only…
The purpose of this memoir is to discuss two very interesting properties of integer sequences. One is the law of apparition and the other is the law of repetition. Both have been extensively studied by mathematicians such as Ward, Lucas,…
Frieze patterns have attracted significant attention recently, motivated by their relationship with cluster algebras. A longstanding open problem has been to provide a combinatorial model for frieze patterns over the ring of integers modulo…
We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…
Motivated by a question of van der Poorten about the existence of infinite chain of prime numbers (with respect to some base), in this paper we advance the study of sequences of consecutive polynomials whose coefficients are chosen…
We prove that all correlations of the sequence of Farey fractions exist and provide formulas for the correlation measures.
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincar\'e duality and hard Lefschetz theorem), and their relations and applications to integral…
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are convergent in…
The number of ordered factorizations and the number of recursive divisors are two related arithmetic functions that are recursively defined. But it is hard to construct explicit representations of these functions. Taking advantage of their…
This paper defines a new sequence of finite dimensional algebras as quotients of the group algebras of the braid groups. This sequence depends on three homogeneous parameters and has a one-parameter family of Markov traces, and so gives a…
A new algebraic object is introduced - recurrent fractions, which is an n-dimensional generalization of continued fractions. It is used to describe an algorithm for rational approximations of algebraic irrational numbers. Some…
The interpretation of data in terms of multi-parameter models of new physics, using the Bayesian approach, requires the construction of multi-parameter priors. We propose a construction that uses elements of Bayesian reference analysis. Our…
Poset-theoretic generalizations of set-theoretic committee constructions are presented. The structure of the corresponding subposets is described. Sequences of irreducible fractions associated to the principal order ideals of finite bounded…
We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given 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 direct application of the definition of sorting in lattices is impractical because it leads to an algorithm with exponential complexity. In this paper we present for distributive lattices a recursive formulation to compute the sort of a…
Distance-based approaches in phylogenetics such as Neighbor-Joining are a fast and popular approach for building trees. These methods take pairs of sequences from them construct a value that, in expectation, is additive under a stochastic…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…