7 papers
Cyclically ordered quivers
Sergey Fomin, Scott Neville
A cyclically ordered quiver is a quiver endowed with an additional structure of a cyclic ordering of its vertices. This structure, which naturally arises in many important applicat…
Eventual sign coherence
Amanda Burcroff, Scott Neville
The sign coherence of -vectors is one of the fundamental theorems of cluster algebras with principal coefficients. In 2019, Gekhtman and Nakanishi posed the asymptotic sign cohe…
Mysterious points in keys but not trees
Scott Neville, José Simental
The deep locus of a cluster variety is defined to be the set of its points that do not belong to any cluster torus. We show that, if the cluster variety has a seed whose mutable pa…
Mutation-acyclic quivers are totally proper
Scott Neville
Totally proper quivers, introduced by S.~Fomin and the author arXiv:2406.03604, have many useful properties including powerful mutation invariants. We show that every mutation-acyc…
Long mutation cycles
Sergey Fomin, Scott Neville
A mutation cycle is a cycle in a graph whose vertices are labeled by the quivers in a given mutation class and whose edges correspond to single mutations. For any fixed , w…
On the phase diagram of the polymer model
Arjun Krishnan, Sevak Mkrtchyan, Scott Neville
In dimensions 3 or larger, it is a classical fact that the directed polymer model has two phases: Brownian behavior at high temperature, and non-Brownian behavior at low temperatur…