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math.CO2026
Coset geometries acting on their elements: The -diagonals twisting
Claudio Alexandre Piedade, Philippe Tranchida
Let be a coset incidence system and fix a type . We use the orbits of the group of on pairs of distinct -elements to define a Coxeter graph. The action on the -ele…
math.CO2025
Geometries with trialities arising from linear spaces
Rémi Delaby, Dimitri Leemans, Philippe Tranchida
A triality is a sort of super-symmetry that exchanges the types of the elements of an incidence geometry in cycles of length three. Although geometries with trialities exhibit fasc…
math.CO2024
Constructing new geometries: a generalized approach to halving for hypertopes
Claudio Alexandre Piedade, Philippe Tranchida
Given a residually connected incidence geometry that satisfies two conditions, denoted and , we construct a new geometry with properties similar to those…