bipartiteQuiver -- make a toric quiver on underlying bipartite graph

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 => ..., 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.
- Height => an integer, default value 10, used in conjunction with the option Flow => Random to set the upper limit of the random number generator
Outputs:
- Q, a toric quiver,

Description

This function creates the unique toric quiver whose underlying graph is the complete 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 => {8, 1, 3, 7, 8, 3}                            }
                 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 => {-12, -18, 15, 9, 6}

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.

The source of this document is in ThinSincereQuivers.m2:3279:0.

bipartiteQuiver -- make a toric quiver on underlying bipartite graph

Description

See also

For the programmer