# leafColorings -- list the consistent colorings of a tree

## Synopsis

• Usage:
leafColorings(T,M)
leafColorings(n,M)
• Inputs:
• T, an instance of the type LeafTree,
• n, an integer, the number of leaves
• M, an instance of the type Model,
• Outputs:
• a list, the consistent colorings of the 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