6 papers
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…
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…
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…
The Automorphism Conjecture for Ordered Sets of Width
Bernd Schröder
We prove the automorphism conjecture for ordered sets of width less than or equal to 11. The proof supports the meta conjecture that a large number of automorphisms is achievable o…
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…
Nonisomorphic Ordered Sets with Arbitrarily Many Ranks That Produce Equal Decks
Bernd Schröder
We prove that for any there is a pair of nonisomorphic ordered sets such that and have equal maximal and minimal decks, equal neighborh…