maximalUnstableSubquivers -- return the maximal subquivers that are unstable

Synopsis

Usage:

maximalUnstableSubquivers Q
Inputs:
- Q, an instance of the type ToricQuiver,
Optional inputs:
- ReturnSingletons => a Boolean value, default value false, Whether or not to return singleton vertices subquivers
- Format => a string, default value "list", format for representing the subquivers
Outputs:
- L, a hash table, consisting of two keys: Nonsingletons and Singletons

Description

This method takes all of the possible subquivers of a given quiver Q and returns those that are both unstable and maximal with respect to the weight on the quiver Q.

Subquivers are represented by lists of arrows, except in the case of subquivers that consist of singleton vertices.

i1 : maximalUnstableSubquivers bipartiteQuiver (2, 3)

o1 = HashTable{NonSingletons => {{0, 1, 2, 3}, {0, 1, 2, 4}, {0, 1, 2, 5}, {0, 3, 4, 5}, {1, 3, 4, 5}, {2, 3, 4, 5}}}

o1 : HashTable

For the programmer

The object maximalUnstableSubquivers is a function closure.