4 papers
The Arithmetic-Periodicity of \textsc{cut} for
Paul Ellis, Thotsaporn Aek Thanatipanonda
\textsc{cut} is a class of partition games played on a finite number of finite piles of tokens. Each version of \textsc{cut} is specified by a cut-set $\mathcal{C}\subseteq\mathbb{…
Reducing the dichromatic number via cycle reversions in infinite digraphs
Paul Ellis, Attila Joó, Dániel T. Soukup
We prove the following conjecture of S. Thomassé: for every (potentially infinite) digraph it is possible to iteratively reverse directed cycles in such a way that the dichro…
Conjugacy for homogeneous ordered graphs
Samuel Coskey, Paul Ellis
We show that for any countable homogeneous ordered graph , the conjugacy problem for automorphisms of is Borel complete. In fact we establish that each such satisfies a…
The Classification Problem for Simple Unital Finite Rank Dimension Groups
Paul Ellis
The Borel complexity of the isomorphism problem for finite-rank unital simple dimension groups increases with rank. This implies that the isomorphism problems for the corresponding…