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leafColorings -- list the consistent colorings of a tree

Description

This function outputs a list of all consistent colorings of the leaves of tree T. That is all sequences $(g_1,\ldots,g_n)$ such that $g_1+\cdots +g_n = 0$ where each $g_i$ is an element of the group associated to the model M, and n is the number of leaves of the tree.

These correspond the set of subscripts of the variables in the ring output by qRing, and appear in the same order.

i1 : leafColorings(4,CFNmodel)

o1 = {(0, 0, 0, 0), (0, 0, 1, 1), (0, 1, 0, 1), (0, 1, 1, 0), (1, 0, 0, 1),
     ------------------------------------------------------------------------
     (1, 0, 1, 0), (1, 1, 0, 0), (1, 1, 1, 1)}

o1 : List
 
i2 : leafColorings(3,JCmodel)

o2 = {({0, 0}, {0, 0}, {0, 0}), ({0, 0}, {0, 1}, {0, 1}), ({0, 0}, {1, 0},
     ------------------------------------------------------------------------
     {1, 0}), ({0, 0}, {1, 1}, {1, 1}), ({0, 1}, {0, 0}, {0, 1}), ({0, 1},
     ------------------------------------------------------------------------
     {0, 1}, {0, 0}), ({0, 1}, {1, 0}, {1, 1}), ({0, 1}, {1, 1}, {1, 0}),
     ------------------------------------------------------------------------
     ({1, 0}, {0, 0}, {1, 0}), ({1, 0}, {0, 1}, {1, 1}), ({1, 0}, {1, 0}, {0,
     ------------------------------------------------------------------------
     0}), ({1, 0}, {1, 1}, {0, 1}), ({1, 1}, {0, 0}, {1, 1}), ({1, 1}, {0,
     ------------------------------------------------------------------------
     1}, {1, 0}), ({1, 1}, {1, 0}, {0, 1}), ({1, 1}, {1, 1}, {0, 0})}

o2 : List

See also

Ways to use leafColorings:

  • leafColorings(LeafTree,Model)
  • leafColorings(ZZ,Model)

For the programmer

The object leafColorings is a method function.

The source of this document is in PhylogeneticTrees.m2:1144:0.