Claudio Alexandre Piedade

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20182026

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4 papers · 1 filter

math.CO2026

Coset geometries acting on their elements: The $j$ -diagonals twisting

Claudio Alexandre Piedade, Philippe Tranchida

Let $β$ be a coset incidence system and fix a type $j$ . We use the orbits of the group of $β$ on pairs of distinct $j$ -elements to define a Coxeter graph. The action on the $j$ -ele…

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.CO2024

Constructing new geometries: a generalized approach to halving for hypertopes

Claudio Alexandre Piedade, Philippe Tranchida

Given a residually connected incidence geometry $Γ$ that satisfies two conditions, denoted $(B_{1})$ and $(B_{2})$ , we construct a new geometry $H (Γ)$ with properties similar to those…

math.CO2021

Infinite families of hypertopes from centrally symmetric polytopes

Claudio Alexandre Piedade

We construct infinite families of abstract regular polytopes of type ${4, p_{1}, \dots, p_{n - 1}}$ from extensions of centrally symmetric spherical abstract regular $n$ -polytopes. In…

Coset geometries acting on their elements: The j-diagonals twisting

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

Constructing new geometries: a generalized approach to halving for hypertopes

Infinite families of hypertopes from centrally symmetric polytopes

Coset geometries acting on their elements: The $j$ -diagonals twisting

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