Polynomial invariants for trees. A statistical mechanics approach (Q1382267)

This paper defines two distinct ways of relating polynomial invariants of trees. Starting from a root point any point of the tree can be reached by successive steps and each step is associated with a recurrence relation---the procedure being analogous to that for defining braids and knots. The work is compared with \textit{W. T. Tutte}'s result in [Can. J. Math. 6, 80-91 (1954; Zbl 0055.17101)] that the dichromate polynomial of any graph can be expressed as a sum over weight trees of the graph. Reviewer notes: The important point is that we must order the lines of a graph in some predetermined way, but the final result for the Whitney-Tutte dichromate polynomial alias Potts model generating function is independent of the order in which we list the lines. Some work by the reviewer gives a clue about the reason for this independence.