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Full-Text Articles in Mathematics
On The Classification Of Vertex-Transitive Structures, John Clemens, Samuel Coskey, Stephanie Potter
On The Classification Of Vertex-Transitive Structures, John Clemens, Samuel Coskey, Stephanie Potter
Mathematics Faculty Publications and Presentations
We consider the classification problem for several classes of countable structures which are “vertex-transitive”, meaning that the automorphism group acts transitively on the elements. (This is sometimes called homogeneous.) We show that the classification of countable vertex-transitive digraphs and partial orders are Borel complete. We identify the complexity of the classification of countable vertex-transitive linear orders. Finally we show that the classification of vertex-transitive countable tournaments is properly above E0 in complexity.
Arithmagons And Geometrically Invariant Multiplicative Integer Partitions, J. A. Franco, J. Champion, J. W. Lyons
Arithmagons And Geometrically Invariant Multiplicative Integer Partitions, J. A. Franco, J. Champion, J. W. Lyons
Mathematics Faculty Publications and Presentations
In this article, we introduce a formal definition for integral arithmagons. Informally, an arithmagon is a polygonal figure with integer labeled vertices and edges in which, under a binary operation, adjacent vertices equal the included edge. By considering the group of automorphisms for the associated graph, we count the number of integral arithmagons whose exterior sum or product equals a fixed number.