6 citations · 17 across the 8 of their papers we have counts for
8 papers
Convex geometry over ordered hyperfields
James Maxwell, Ben Smith
We initiate the study of convex geometry over ordered hyperfields. We define convex sets and halfspaces over ordered hyperfields, presenting structure theorems over hyperfields ari…
Root polytopes, tropical types, and toric edge ideals
Ayah Almousa, Anton Dochtermann, Ben Smith
We consider arrangements of tropical hyperplanes where the apices of the hyperplanes are taken to infinity in certain directions. Such an arrangement defines a decomposition of Euc…
On complete classes of valuated matroids
Edin Husić, Georg Loho, Ben Smith +1
We characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking…
Face posets of tropical polyhedra and monomial ideals
Georg Loho, Ben Smith
We exhibit several posets arising from commutative algebra, order theory, tropical convexity as potential face posets of tropical polyhedra, and we clarify their inclusion relation…
Convergent Hahn Series and Tropical Geometry of Higher Rank
Michael Joswig, Ben Smith
We propose to study the tropical geometry specifically arising from convergent Hahn series in multiple indeterminates. One application is a new view on stable intersections of trop…
Matching fields and lattice points of simplices
Georg Loho, Ben Smith
We show that the Chow covectors of a linkage matching field define a bijection between certain degree vectors and lattice points, and we demonstrate how one can recover the linkage…
Computing Tropical Varieties in Macaulay2
Carlos Améndola, Kathlén Kohn, Sara Lamboglia +5
We introduce a package for doing tropical computations in Macaulay2. The package draws on the functionality of Gfan and Polymake while making the process as simple as possible for…
Commutative Algebra of Generalised Frobenius Numbers
Madhusudan Manjunath, Ben Smith
We study commutative algebra arising from generalised Frobenius numbers. The -th (generalised) Frobenius number of natural numbers is the largest natural numbe…