215 citations · 640 across the 23 of their papers we have counts for
24 papers
Characteristic Sets of Matroids
Dustin Cartwright, Dony Varghese
We investigate possible linear, algebraic, and Frobenius flock characteristic sets of matroids. In particular, we classify possible combinations of linear and algebraic characteris…
Matroids over one-dimensional groups
Guus P. Bollen, Dustin Cartwright, Jan Draisma
We develop the theory of matroids over one-dimensional algebraic groups, with special emphasis on positive characteristic. In particular, we compute the Lindström valuations and Fr…
Construction of the Lindström valuation of an algebraic extension
Dustin Cartwright
Recently, Bollen, Draisma, and Pendavingh have introduced the Lindström valuation on the algebraic matroid of a field extension of characteristic p. Their construction passes throu…
A specialization inequality for tropical complexes
Dustin Cartwright
We prove a specialization inequality relating the dimension of the complete linear series on a variety to the tropical complex of a regular semistable degeneration. Our result exte…
Excluded homeomorphism types for dual complexes of surfaces
Dustin Cartwright
We study an obstruction to prescribing the dual complex of a strict semistable degeneration of an algebraic surface. In particular, we show that if is a complex homeomorphic to…
Combinatorial tropical surfaces
Dustin Cartwright
We study the combinatorial properties of 2-dimensional tropical complexes. In particular, we prove tropical analogues of the Hodge index theorem and Noether's formula. In addition,…