bipartiteQuiver -- make a toric quiver on underlying bipartite graph

Synopsis

Usage:

bipartiteQuiver (N, M)
Inputs:
- N, an integer, number of vertices that are sources
- M, an integer, number of vertices that are sinks
Optional inputs:
- Flow (missing documentation) => ..., default value "Canonical", specify what form of flow to use. This input can be either a string with values Canonical or Random, or else a list of integer values.
Outputs:
- Q, an instance of the type ToricQuiver,

Description

This function creates the unique toric quiver whose underlying graph is the fully connected bipartite graph with N source vertices and M sink vertices.

i1 : Q = bipartiteQuiver (2, 3)

o1 = ToricQuiver{flow => {1, 1, 1, 1, 1, 1}                            }
                 IncidenceMatrix => | -1 -1 -1 0  0  0  |
                                    | 0  0  0  -1 -1 -1 |
                                    | 1  0  0  1  0  0  |
                                    | 0  1  0  0  1  0  |
                                    | 0  0  1  0  0  1  |
                 Q0 => {0, 1, 2, 3, 4}
                 Q1 => {{0, 2}, {0, 3}, {0, 4}, {1, 2}, {1, 3}, {1, 4}}
                 weights => {-3, -3, 2, 2, 2}

o1 : ToricQuiver

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

o2 = ToricQuiver{flow => {24, 65, 71, 72, 19, 19}                      }
                 IncidenceMatrix => | -1 -1 -1 0  0  0  |
                                    | 0  0  0  -1 -1 -1 |
                                    | 1  0  0  1  0  0  |
                                    | 0  1  0  0  1  0  |
                                    | 0  0  1  0  0  1  |
                 Q0 => {0, 1, 2, 3, 4}
                 Q1 => {{0, 2}, {0, 3}, {0, 4}, {1, 2}, {1, 3}, {1, 4}}
                 weights => {-160, -110, 96, 84, 90}

o2 : ToricQuiver

i3 : Q = bipartiteQuiver (2, 3, Flow=>{1, 2, 1, 3, 1, 4})

o3 = ToricQuiver{flow => {1, 2, 1, 3, 1, 4}                            }
                 IncidenceMatrix => | -1 -1 -1 0  0  0  |
                                    | 0  0  0  -1 -1 -1 |
                                    | 1  0  0  1  0  0  |
                                    | 0  1  0  0  1  0  |
                                    | 0  0  1  0  0  1  |
                 Q0 => {0, 1, 2, 3, 4}
                 Q1 => {{0, 2}, {0, 3}, {0, 4}, {1, 2}, {1, 3}, {1, 4}}
                 weights => {-4, -8, 4, 3, 5}

o3 : ToricQuiver

For the programmer

The object bipartiteQuiver is a function closure.