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math.CO2023
Sparse groups need not be semisparse
Isabel Hubard, Micael Toledo
In 1999 Michael Hartley showed that any abstract polytope can be constructed as a double coset poset, by means of a C-group $\C$ and a subgroup $N \leq \C$. Subgroups $N \leq \C$ t…
math.CO2023
Transitive cornerations in maps
Primoz Potocnik, Alejandra Ramos-Rivera, Micael Toledo +1
A corner in a map is an edge-vertex-edge triple consisting of two distinct edges incident to the same vertex. A corneration is a set of corners that covers every arc of the map exa…
math.CO2023
Faithful and thin non-polytopal maniplexes
Dimitri Leemans, Micael Toledo
Maniplexes are coloured graphs that generalise maps on surfaces and abstract polytopes. Each maniplex uniquely defines a partially ordered set that encodes information about its st…