# isTight -- determine if toric quiver is tight

## Synopsis

• Usage:
isTight Q
isTight(Q, W)
isTight(W, Q)
• Inputs:
• 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:

## 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 .