31 citations · 32 across the 8 of their papers we have counts for
12 papers
Representing alternating groups as self-dual string C-groups of high rank
Gabe Cunningham, Mark Mixer
The highest rank of a string C-group representation of the alternating group is known for each , but no self-dual representations attaining this highest rank are known whe…
Conditional Probability of Derangements and Fixed Points
Sam Gutmann, Mark Mixer, Steven Morrow
The probability that a random permutation in is a derangement is well known to be . In this paper, we consider the condi…
Vertex-Faithful Regular Polyhedra
Gabe Cunningham, Mark Mixer
We study the abstract regular polyhedra with automorphism groups that act faithfully on their vertices, and show that each non-flat abstract regular polyhedron covers a "vertex-fai…
The ranks of alternating string C-groups
Mark Mixer
In this paper, string C-groups of all ranks are provided for each alternating group , . As the string C-group representations of h…
Archimedean toroidal maps and their minimal almost regular covers
Kostiantyn Drach, Yurii Haidamaka, Mark Mixer +1
The automorphism group of a map acts naturally on its flags (triples of incident vertices, edges, and faces). An Archimedean map on the torus is called almost regular if it has as…
Internal and external duality in abstract polytopes
Gabe Cunningham, Mark Mixer
We define an abstract regular polytope to be internally self-dual if its self-duality can be realized as one of its symmetries. This property has many interesting implications on t…