6 papers
Matroidal representations of low rank
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We study tropical subrepresentations of the Boolean regular representation of a finite group . These are equivalent to the matroids on ground set for which l…
Tropical representations and valuated matroids
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We explore several facets of tropical subrepresentations of a linear representation of a group over the tropical semifield . A key role in the study of tropical subrepr…
Representation theory over semifields
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We study and classify representations of a torsion group over an idempotent semifield with special attention on the case over the Boolean semifield . In subsequent…
Equivariant vector bundles on toric schemes over semirings
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric ve…
Facets of module theory over semirings
James Borger, Jaiung Jun
We set up some basic module theory over semirings, with particular attention to what is needed in scheme theory over semirings. We show that while not all the usual definitions of…
Artin-Ihara L-functions for hypergraphs
Mason Eyler, Jaiung Jun
We generalize Artin-Ihara L-functions for graphs to hypergraphs by exploring several analogous notions, such as (unramified) Galois coverings and Frobenius elements. To a hypergrap…