12 papers
Roots in the substitution group and in the group of Riordan matrices with ones in the main diagonal
Jorge Calero-Sanz, Luis Felipe Prieto-Martínez
We investigate the existence and uniqueness of iterative roots of order within the substitution group of formal power series -- with coefficients in a commutati…
Riordan pattern's quest within simplicial complexes
Pedro J. Chocano, Ana Luzón, Manuel A. Morón +1
The aim of this paper is twofold. First, we demonstrate how Riordan matrices can be employed to connect well-known concepts in geometric combinatorics, such as -vectors, -vec…
Bi-infinite Riordan matrices: a matricial approach to multiplication and composition of Laurent series
Luis Felipe Prieto-Martínez, Javier Rico
We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infi…
On the concept of center for geometric objects and related problems
M. Magdalena Martínez-Rico, L. Felipe Prieto-Martínez, R. Sánchez-Cauce
In this work, we review the concept of center of a geometric object as an equivariant map, unifying and generalizing different approaches followed by authors such as C. Kimberling…
The concept of center as an equivariant map and a proof of an analogue of the center conjecture for equifacetal simplices
Luis Felipe Prieto-Martínez
Several authors have remarked the convenience of understanding the different notions of center appearing in Geometry (centroid of a set of points, incenter of a triangle, center of…
A Rellich's result revisited and sensitivity of solutions of parametrized linear systems
José Carlos Bellido, Luis Felipe Prieto-Martínez
In this paper we revisit a result due to Franz Rellich on smoothness of solutions of parametrized linear systems. With this result as a starting point, we obtain finer smoothness r…
The relation between symmetries and coincidence and collinearity of polygon centers and centers of multisets of points in the plane
Luis Felipe Prieto-Martínez
There are several remarkable points, defined for polygons and multisets of points in the plane, called centers (such as the centroid). To make possible their study, there exists a…
-gon centers and central lines
Marta Farré Puiggalí, Luis Felipe Prieto-Martínez
In this paper we provide a review of the concept of center of a -gon, generalizing the original idea given by C. Kimberling for triangles. We also generalize the concept of cent…
Circular arcs are the only analytic Jordan curves with an exterior power point
Luis Felipe Prieto-Martínez
In 1946, J. Rosenbaum proposed a family of problems asking how many power points are needed to ensure that the boundary of a given convex body is a disk. In this paper, we use…
Commutators and commutator subgroups of the Riordan group
Ana Luzón, Manuel A. Morón, Luis Felipe Prieto-Martínez
We calculate the derived series of the Riordan group. To do that, we study a nested sequence of its subgroups, herein denoted by . By means of this sequence, we first…
A list of problems in Plane Geometry with simple statement that remain unsolved
Luis Felipe Prieto-Martínez
This article contains a short and entertaining list of unsolved problems in Plane Geometry. Their statement may seem naive and can be understood at an elementary level. But their s…
Geometric continuity of plane curves in terms of Riordan matrices and an application to the F-chordal problem
Luis Felipe Prieto-Martínez
The first goal of this article is to provide an statement of the conditions for geometric continuity of order k, referred in the bibliography as beta-constraints, in terms of Riord…