chainQuiver -- make a toric quiver on underlying graph in the form of a chain

Synopsis

Usage:

chainQuiver E
Inputs:
- E, a list, number of edges linking each vertex to the next
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.
Outputs:
- Q, an instance of the type ToricQuiver,

Description

A chain quiver is a quiver where each vertex N is connected to its predecessor vertex N - 1 by arrows pointing from N - 1 to N, and connected to its successor vertex N + 1 by arrows pointing to N + 1. This results in a quiver in the shape of a chain, where each pair of vertices along the chain is connected by a variable number of edges.

i1 : Q = chainQuiver {1,2,3}

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

o1 : ToricQuiver

i2 : Q = chainQuiver ({1,2,3}, Flow => "Random")

o2 = ToricQuiver{flow => {8, 1, 3, 7, 8, 3}                            }
                 IncidenceMatrix => | -1 0  0  0  0  0  |
                                    | 1  -1 -1 0  0  0  |
                                    | 0  1  1  -1 -1 -1 |
                                    | 0  0  0  1  1  1  |
                 Q0 => {0, 1, 2, 3}
                 Q1 => {{0, 1}, {1, 2}, {1, 2}, {2, 3}, {2, 3}, {2, 3}}
                 synonym => toric quiver
                 weights => {-8, 4, -14, 18}

o2 : ToricQuiver

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

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

o3 : ToricQuiver

For the programmer

The object chainQuiver is a function closure.

chainQuiver -- make a toric quiver on underlying graph in the form of a chain

Synopsis

Description

See also

For the programmer