Claudio Alexandre Piedade

• PhD in Mathematics
• Researcher at Centro de Matemática da Universidade do Porto

In this paper, we list all possible degrees of a faithful transitive permutation representation of the group of symmetries of a regular map of types {4,4}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsid...

We give a list of all possible degrees of faithful transitive permutation representations, corresponding to the indexes of core-free subgroups, of the finite universal regular polytopes ${{4,4}_{(t_1,t_2)},{4,4}_{(s_1,s_2)}}$.

We construct infinite families of abstract regular polytopes of Schläfli type $\{4,p_1,\ldots,p_{n-1}\}$ from extensions of centrally symmetric spherical abstract regular $n$-polytopes. In addition, by applying the halving operation, we obtain infinite families of both locally spherical and locally toroidal regular hypertopes of type $\left\{\genfr...

Given a residually connected incidence geometry $\Gamma$ that satisfies two conditions, denoted $(B_1)$ and $(B_2)$, we construct a new geometry $H(\Gamma)$ with properties similar to those of $\Gamma$. This new geometry $H(\Gamma)$ is inspired by a construction of Percsy, Percsy and Leemans [1]. We show how $H(\Gamma)$ relates to the classical hal...

Previous research established that the maximal rank of the abstract regular polytopes whose automorphism group is a transitive proper subgroup of $\Sym_n$ is $n/2 + 1$, with only two polytopes attaining this rank, both of which having odd ranks. In this paper, we investigate the case where the rank is equal to $n/2$ ($n\geq 14$). Our analysis revea...

Given a residually connected incidence geometry that satisfies two conditions, denoted and , we construct a new geometry with properties similar to those of . This new geometry is inspired by a construction of Lefèvre-Percsy, Percsy and Leemans (Bull Belg Math Soc Simon Stevin 7(4):583–610, 2000). We show how relates to the classical halving operat...

In this paper we give a non-computer-assisted proof of the following result: if G is an even transitive group of degree 11 and has a string C-group representation with rank r ∈ {4, 5} then G ≅ PSL2(11). Moreover this string C-group is the group of automorphisms of the rank 4 polytope known as the 11-cell. The insights gained from this case study in...

This paper is an exploration of the faithful transitive permutation representations of the orientation-preserving automorphisms groups of highly symmetric toroidal maps and hypermaps. The main theorems of this paper give a list of all possible degrees of these specific groups. This extends prior accomplishments of the authors, wherein their focus w...

The list of degrees of a faithful transitive permutation representation for the map

We construct infinite families of abstract regular polytopes of type $\{4,p_1,\ldots,p_{n-1}\}$ from extensions of centrally symmetric spherical abstract regular $n$-polytopes. In addition, by applying the halving operation, we obtain infinite families of both locally spherical and locally toroidal regular hypertopes of type $\left\{{p_1 \atop p_1}...

Recently the classification of all possible faithful transitive permutation representations of the group of symmetries of a regular toroidal map was accomplished. In this paper we complete this investigation on a surface of genus 1 considering the group of a regular toroidal hypermap of type $(3,3,3)$ that is a subgroup of index $2$ of the group of...

Virus are supramolecular structures that are responsible for some of the most significant epidemics around the world. The disassembly of virus particles, a key event during viral infection is triggered by numerous intracellular factors. The investigation of the mechanisms of protein subunit loss during viral disassembly has generally been overlooke...