37 research outputs found
Simple permutations with order . Part I
The problem of genealogy of permutations has been solved partially by Stefan
(odd order) and Acosta-Hum\'anez & Bernhardt (power of two). It is well known
that Sharkovskii's theorem shows the relationship between the cardinal of the
set of periodic points of a continuous map, but simple permutations will show
the behavior of those periodic points. This paper studies the structure of
permutations of mixed order , its properties and a way to describe its
genealogy by using Pasting and Reversing.Comment: 17 page
Pasting and Reversing Approach to Matrix Theory
The aim of this paper is to study some aspects of matrix theory through
Pasting and Reversing. We start giving a summary of previous results concerning
to Pasting and Reversing over vectors and matrices, after we rewrite such
properties of Pasting and Reversing in matrix theory using linear mappings to
finish with new properties and new sets in matrix theory involving Pasting and
Reversing. In particular we introduce new linear mappings: Palindromicing and
Antipalindromicing mappings, which allow us to obtain palindromic and
antipalindromic vectors and matrices.Comment: 19 page
Some Remarks on a Generalized Vector Product
In this paper we use a generalized vector product to construct an exterior
form , where
, . Finally, for we
introduce the reversing operation to study this generalized vector product over
palindromic and antipalindromic vectors.Comment: 10 pages, 14 pages in the published version: Revista Integraci\'o
Variations for Some Painlev\'e Equations
This paper first discusses irreducibility of a Painlev\'e equation . We
explain how the Painlev\'e property is helpful for the computation of special
classical and algebraic solutions. As in a paper of Morales-Ruiz we associate
an autonomous Hamiltonian to a Painlev\'e equation . Complete
integrability of is shown to imply that all solutions to are
classical (which includes algebraic), so in particular is solvable by
''quadratures''. Next, we show that the variational equation of at a given
algebraic solution coincides with the normal variational equation of
at the corresponding solution. Finally, we test the Morales-Ramis
theorem in all cases to where algebraic solutions are present,
by showing how our results lead to a quick computation of the component of the
identity of the differential Galois group for the first two variational
equations. As expected there are no cases where this group is commutative