isTight -- determine if toric quiver is tight

Synopsis

Usage:

isTight Q

isTight(Q, W)

isTight(W, Q)
Inputs:
- Q, an instance of the type ToricQuiver,
- W, a list,
Optional inputs:
- Format (missing documentation) => ..., default value Flow, specify whether input W is a flow (integer values associated to each arrow) or the image of the flow under the map theta (integer values associated to each vertex).
Outputs:
- a Boolean value,

Description

A toric quiver $Q$ is tight with respect to a given flow if there is no maximal unstable subquiver of codimension 1. That is, every unstable subquiver of $Q$ has at most $|Q_1|-2$ arrows. This method determines if a toric quiver $Q$ is tight with respect to the vertex weights induced by its flow.

i1 : isTight bipartiteQuiver(2, 3)

o1 = true

i2 : isTight bipartiteQuiver(2, 3, Flow=>"Random")

o2 = true

i3 : isTight (bipartiteQuiver(2, 3), {2,1,2,3,2,3})

o3 = true

i4 : isTight ({2,1,2,3,2,3}, bipartiteQuiver(2, 3))

o4 = true

Ways to use `isTight` :

"isTight(List,ToricQuiver)"
"isTight(ToricQuiver)"
"isTight(ToricQuiver,List)"

For the programmer

The object isTight is a method function with options.

isTight -- determine if toric quiver is tight

Synopsis

Description

Ways to use isTight :

For the programmer

Ways to use `isTight` :