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math.CO2023
Small Representations of Permutation Groups by Embedding the Domain in an Ordered Set
Bernd Schröder
We present a representation for permutation groups as the automorphism group of an ordered set such that the automorphism group's action on a subset is the permu…
math.CO2023
Towards the Automorphism Conjecture I: Combinatorial Control
Bernd S. W. Schröder
This paper exploits adjacencies between the orbits of an ordered set P and a consequence of the classification of finite simple groups to, in many cases, exponentially bound the nu…
math.CO2023
The Automorphism Conjecture for Ordered Sets of Width (Version 2)
Bernd S. W. Schröder
We introduce a recursive method to deconstruct the automorphism group of an ordered set. By connecting this method with deep results for permutation groups, we prove the Automorphi…