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ThinSincereQuivers :: allSpanningTrees

allSpanningTrees -- find the spanning trees of the underlying graph

Synopsis

Description

This method returns all of the spanning trees of the underlying graph of the quiver Q. Trees are represented as lists of arrow indices.

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 : allSpanningTrees(Q)

o2 = {{2, 3, 4, 5}, {1, 3, 4, 5}, {0, 3, 4, 5}, {0, 2, 4, 5}, {0, 1, 4, 5},
     ------------------------------------------------------------------------
     {1, 2, 3, 5}, {0, 1, 3, 5}, {0, 1, 2, 5}, {1, 2, 3, 4}, {0, 2, 3, 4},
     ------------------------------------------------------------------------
     {0, 1, 2, 4}, {0, 1, 2, 3}}

o2 : List

For the programmer

The object allSpanningTrees is a function closure.