4 papers
A matroidal twist on a formula of Brion
Matthias Beck, Caroline Klivans, Dustin Ross
Brion's Formula realizes the Laurent polynomial of lattice points in a lattice polytope P as the sum of rational functions associated to the vertices of P. In this paper, we consid…
K-rings of smooth toric varieties via piecewise-exponential functions
Melody Chan, Emily Clader, Caroline Klivans +1
We describe an explicit presentation of the ring of integral piecewise-exponential functions on a unimodular fan as a quotient of the Stanley-Reisner ring of the fan. This gives ri…
Piecewise-exponential functions and Ehrhart fans
Melody Chan, Emily Clader, Caroline Klivans +1
This paper studies rings of integral piecewise-exponential functions on rational fans. Motivated by lattice-point counting in polytopes, we introduce a special class of unimodular…
On the topology of no -equal spaces
Yuliy Baryshnikov, Caroline Klivans, Nicholas Kosar
We consider the topology of real no -equal spaces via the theory of cellular spanning trees. Our main theorem proves that the rank of the -dimensional homology of the no…