29 citations · 185 across the 37 of their papers we have counts for
6 papers · 1 filter
Quiver matroids -- Matroid morphisms, quiver Grassmannians, their Euler characteristics and -points
Manoel Jarra, Oliver Lorscheid, Eduardo Vital
In this paper, we introduce morphisms for matroids with coefficients (in the sense of Baker and Bowler) and quiver matroids. We investigate their basic properties, such as functori…
Towards the horizons of Tits's vision -- on band schemes, crowds and F1-structures
Oliver Lorscheid, Koen Thas
This text is dedicated to Jacques Tits's ideas on geometry over F1, the field with one element. In a first part, we explain how thin Tits geometries surface as rational point sets…
Flag matroids with coefficients
Manoel Jarra, Oliver Lorscheid
This paper is a direct generalization of Baker-Bowler theory to flag matroids, including its moduli interpretation as developed by Baker and the second author for matroids. More ex…
Lift theorems for representations of matroids over pastures
Matthew Baker, Oliver Lorscheid
Pastures are a class of field-like algebraic objects which include both partial fields hyperfields and have nice categorical properties. We prove several lift theorems for represen…
Foundations of matroids I: Matroids without large uniform minors
Matthew Baker, Oliver Lorscheid
The foundation of a matroid is a canonical algebraic invariant which classifies representations of the matroid up to rescaling equivalence. Foundations of matroids are pastures, a…
On the relation between hyperrings and fuzzy rings
Jeffrey Giansiracusa, Jaiung Jun, Oliver Lorscheid
We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings and explicitly characterize the essential image --- it fails to be essentially sur…