wallType -- get the type of a wall for a given quiver

Usage:

wallType (Qplus, Q)

wallType (Qplus, M)

wallType (W)
Inputs:
- Q, a toric quiver,
- M, a matrix,
- Qplus, a list,
- W, a wall (missing documentation) ,
Outputs:
- WT, a sequence, having two nonnegative integer entries denoting the type of the wall

Description

Every wall can be represented uniquely by a partition of the vertices Q0 of Q into two sets Qplus and Qminus. We denote the wall W by the subset of vertices Qplus used for defining it.

The type of the wall is defined as (t+,t-) where t^+ is the number of arrows starting Qplus and ending in Qminus, and t- is the number of arrows starting Qminus and ending in Qplus.

This method is written to compute the wall type based on the incidence matrix, in the case of a trivial flow, or the entire quiver. It will also return the type for a given wall.

i1 : wallType({0,2,3}, bipartiteQuiver(2, 3))

o1 = (1, 2)

o1 : Sequence

i2 : wallType({0,2,3}, quiverIncidenceMatrix(bipartiteQuiver(2, 3)))

o2 = (1, 2)

o2 : Sequence

i3 : wallType({1,2,3}, chainQuiver({2,3,4}))

o3 = (0, 2)

o3 : Sequence

i4 : wallType(first potentialWalls chainQuiver({2,3,4}))

o4 = (0, 2)

o4 : Sequence

Ways to use wallType:

wallType(List,Matrix)
wallType(List,ToricQuiver)

For the programmer

The object wallType is a method function.

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