24 citations · 93 across the 20 of their papers we have counts for
4 papers · 1 filter
Tropical curves in sandpiles
Nikita Kalinin, Mikhail Shkolnikov
We study a sandpile model on the set of the lattice points in a large lattice polygon. A small perturbation of the maximal stable state is obtained by adding extra…
Sandpiles on the heptagonal tiling
Nikita Kalinin, Mikhail Shkolnikov
We study perturbations of the maximal stable state in a sandpile model on the set of faces of the heptagonal tiling on the hyperbolic plane. An explicit description for relaxations…
A guide to tropical modifications
Nikita Kalinin
This paper surveys {\it tropical modifications}, a notion that has become part of the folklore of tropical geometry. Tropical modifications are used in tropical intersection theory…
Tropical curves in sandpile models
Nikita Kalinin, Mikhail Shkolnikov
A sandpile is a cellular automaton on a graph that evolves by the following toppling rule: if the number of grains at a vertex is at least its valency, then this vertex sends one g…