3,792 research outputs found
Middle divisors and -palindromic Dyck words
Given a real number , we say that is a -middle
divisor of if We
will prove that there are integers having an arbitrarily large number of
-middle divisors. Consider the word given by where is the set of
divisors of , and are the elements of the symmetric difference written in increasing order. We will prove that the language contains Dyck words having an
arbitrarily large number of centered tunnels. We will show a connection between
both results
A relationship between the ideals of and the Fibonacci numbers
Let be the number of ideals of codimension of
, where is the
finite field with elements. Kassel and Reutenauer [KasselReutenauer2015A]
proved that is a polynomial in for any fixed value of .
For , this combinatorial interpretation of
is lost. Nevertheless, an unexpected connexion with Fibonacci numbers appears.
Let be the -th Fibonacci number (following the convention ,
). Define the series
We will prove that for each ,
where the integers are given by the following generating function
\prod_{m \geq 1} \left(1+F\left( t^m\right)\right) = 1 + \sum_{n \geq 1}
\lambda_n\,t^n. $
On a function introduced by Erd\"{o}s and Nicolas
Erd\"os and Nicolas [erdos1976methodes] introduced an arithmetical function
related to divisors of in short intervals . The aim of this note is to prove that is the largest
coefficient of polynomial introduced by Kassel and Reutenauer
[kassel2015counting]. We deduce that has a coefficient larger than
if and only if is the perimeter of a Pythagorean triangle. We improve a
result due to Vatne [vatne2017sequence] concerning the coefficients of
On prime numbers of the form
Consider the set of integers for which there are infinitely
many primes such that is a power of . The aim of this paper is to
show a relationship between and the limits points of some set
rational numbers related to a sequence of polynomials introduced by
Kassel and Reutenauer [KasselReutenauer]
Factorization of Dyck words and the distribution of the divisors of an integer
In [CaballeroHooleyDelta], we associated a Dyck word to any pair consisting of an
integer and a real number . The goal of the present
paper is to show a relationship between the factorization of as the concatenation of irreducible Dyck words
and the distribution of the divisors of . In particular, we will provide a
characterization of -densely divisible numbers (these numbers were
introduced in [castryck2014new])
Relative positions of points on the real line and balanced parentheses
Consider a finite set of positive real numbers . For any real number
, a Dyck word denoted , was defined in [CaballeroWords2017] in
order to compute Hooley's -function and its generalization. The aim of
this paper is to prove that, given a real number , any Dyck word
can be expressed as for some
finite set of positive real numbers
Self-Similar Algebras with connections to Run-length Encoding and Rational Languages
A self-similar algebra is an associative
algebra with a morphism of algebras , where is the set of matrices with coefficients from
. We study the connection between self-similar algebras with
run-length encoding and rational languages. In particular, we provide a curious
relationship between the eigenvalues of a sequence of matrices related to a
specific self-similar algebra and the smooth words over a 2-letter alphabet. We
also consider the language of words in
where such that is a unit in . We
prove that is rational and provide an asymptotic formula for the number
of words of a given length in
Responsabilidad en casos de detenciones o privación de libertad con resultado de muerte
Cada vez son más los casos en donde una persona muere durante el forcejeo que mantiene con las Fuerzas y Cuerpos de Seguridad del Estado durante el proceso de detención. Esto supone un gran reto profesional para el médico forense que realiza la autopsia. En muchas ocasiones, los resultados obtenidos tras la autopsia no son entendidos por la sociedad, familiares del fallecido ni correctamente divulgados por los medios de comunicación, pareciendo que dicha muerte queda en un limbo judicial.
Estas muertes, generalmente son consecuencia del síndrome de delirium agitado. Este síndrome no es bien conocido en nuestro país por parte de médicos ni por cuerpos de seguridad. Se engloban dentro de las muertes en privación de libertad o death in custody. En su producción intervienen factores como la patología previa del paciente, consumo de drogas, especialmente cocaína, y la forma de llevar a cabo el proceso de inmovilización del detenido.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
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