Maria Elisa Fernandes

activity

20142025

most citedHighest rank of a polytope for

A_{n}

31 citations · 33 across the 8 of their papers we have counts for

collaborators

14 papers

math.GR2025

The maximal rank of a string group generated by involutions for alternating groups

Jessica Anzanello, Maria Elisa Fernandes, Pablo Spiga

A string group generated by involutions, or SGGI, is a pair $Γ = (G, S)$ , where $G$ is a group and $S = {ρ_{0}, \dots, ρ_{r - 1}}$ is an ordered set of involutions generating $G$ and sat…

math.CO2024

Regular polytopes of rank $n /2$ for transitive groups of degree $n$

Maria Elisa Fernandes, Claudio Alexandre Piedade

Previous research established that the maximal rank of the abstract regular polytopes whose automorphism group is a transitive proper subgroup of $\mbox{S}_n$ is $n /2 + 1$ . Up to i…

math.GR2023

The degrees of the orientation-preserving automorphism groups of toroidal maps and hypermaps

Maria Elisa Fernandes, Claudio Alexandre Piedade

This paper is an exploration of the faithful transitive permutation representations of the orientation-preserving automorphisms groups of highly symmetric toroidal maps and hyperma…

math.GR2023

String C-group representations of transitive Groups: a case study with degree $11$

Maria Elisa Fernandes, Claudio Alexandre Piedade, Olivia Reade

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\…

math.GR2023

The number of string C-groups of high rank

Peter J. Cameron, Maria Elisa Fernandes, Dimitri Leemans

If $G$ is a transitive group of degree $n$ having a string C-group of rank $r \geq (n + 3) /2$ , then $G$ is necessarily the symmetric group $S_{n}$ . We prove that if $n$ is large enough,…

math.GR2020

The Degrees Of Toroidal Regular Proper Hypermaps

Maria Elisa Fernandes, Claudio Alexandre Piedade

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…

math.GR2018

String C-group representations of alternating groups

Maria Elisa Fernandes, Dimitri Leemans

We prove that for any integer $n \geq 12$ , and for every $r$ in the interval $[3, \dots, ⌊(n - 1) /2 ⌋]$ , the group $A_{n}$ has a string C-group representation of rank $r$ t…

math.AG2018

Faithful permutation representations of toroidal regular maps

Maria Elisa Fernandes, Claudio Alexandre Piedade

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 ${4, 4}$ and ${3, 6}$ and we g…

math.GR2016★ 31 cited

Highest rank of a polytope for $A_{n}$

Peter J. Cameron, Maria Elisa Fernandes, Dimitri Leemans +1

We prove that the highest rank of a string C-group constructed from an alternating group $A l t_{n}$ is 0 if $n = 3, 4, 6, 7, 8$ ; 3 if $n = 5$ ; 4 if $n = 9$ ; 5 if $n = 10$ ; 6 if $n = 11$ ; and $\…

math.GR2016

Highly symmetric hypertopes

Maria Elisa Fernandes, Dimitri Leemans, Asia Ivić Weiss

We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the poly…

math.CO2015

C-groups of high rank for the symmetric groups

Maria Elisa Fernandes, Dimitri Leemans

We classify C-groups of ranks $n - 1$ and $n - 2$ for the symmetric group $S_{n}$ . We also show that all these C-groups correspond to hypertopes, that is, thin, residually connected flag…

math.CO2015

An extension of the classification of high rank regular polytopes

Maria Elisa Fernandes, Dimitri Leemans, Mark Mixer

Up to isomorphism and duality, there are exactly two non-degenerate abstract regular polytopes of rank greater than $n - 3$ , one of rank $n - 1$ and one of rank $n - 2$ , with automorphis…

math.GR2014★ 1 cited

Chirality in incidence geometry

Maria Elisa Fernandes, Dimitri Leemans, Asia Ivić Weiss

Guided by the ideas of chirality in the abstract polytope theory, the present paper aims to extend the concept to a more general setting of incidence geometries. The purpose of thi…

math.GR2014★ 1 cited

String C-groups as transitive subgroups of Sym(n)

Peter J. Cameron, Maria Elisa Fernandes, Dimitri Leemans +1

If $Γ$ is a string C-group which is isomorphic to a transitive subgroup of the symmetric group Sym(n) (other than Sym(n) and the alternating group Alt(n)), then the rank of $Γ$ is…

The maximal rank of a string group generated by involutions for alternating groups

Regular polytopes of rank n/2 for transitive groups of degree n

The degrees of the orientation-preserving automorphism groups of toroidal maps and hypermaps

String C-group representations of transitive Groups: a case study with degree 11

The number of string C-groups of high rank

The Degrees Of Toroidal Regular Proper Hypermaps

String C-group representations of alternating groups

Faithful permutation representations of toroidal regular maps

Highest rank of a polytope for An​

Highly symmetric hypertopes

C-groups of high rank for the symmetric groups

An extension of the classification of high rank regular polytopes

Chirality in incidence geometry

String C-groups as transitive subgroups of Sym(n)

Regular polytopes of rank $n /2$ for transitive groups of degree $n$

String C-group representations of transitive Groups: a case study with degree $11$

Highest rank of a polytope for $A_{n}$