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pro vyhledávání: '"Piedade, Claudio Alexandre"'
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 t
Externí odkaz:
http://arxiv.org/abs/2407.16003
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
Externí odkaz:
http://arxiv.org/abs/2405.19050
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 degree
Externí odkaz:
http://arxiv.org/abs/2308.16841
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 $r\in\{4,5\}$ then $G\cong\PSL_2(11)$. Moreover this string C-group is th
Externí odkaz:
http://arxiv.org/abs/2302.11943
Autor:
Piedade, Claudio Alexandre
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 famili
Externí odkaz:
http://arxiv.org/abs/2103.17170
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 gr
Externí odkaz:
http://arxiv.org/abs/2005.08061
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 give examples of graphs, called CPR-graphs, representing some of these
Externí odkaz:
http://arxiv.org/abs/1808.09705
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The alternating group $A_{11}$ is the automorphism group of abstract regular polytopes of rank $3$ and $6$ but not of rank $4$ and $5$. This is the only alternating group that has a gap in the set of possible ranks of abstract regular polytopes. Inde
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::62765f3ca9573ad43f2ad89f2a33e028
http://arxiv.org/abs/2302.11943
http://arxiv.org/abs/2302.11943
Akademický článek
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