3 papers
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.CO2018
Upper Covers of Chains and Antichains in Sets of Indecomposable Subsets
Bernd S. W. Schröder
We prove that there are arbitrarily large indecomposable ordered sets T with a 2-chain C such that the smallest indecomposable proper superset U of C in T is T itself. Subsequently…