There is an identity due to Feynman which relates graphs and closed curves on a lattice and it was used by Feynman in his combinatorial proof of Onsager's closed formula for the partition function of the two-dimensional Ising model, Long ago Sherman considered a special case of this identity and pointed out similarities with the Witt identity of Lie algebra theory. In this paper and following, Ne revisit this special case and solve some problems related with it. In particular, the weights are computed explicitly using paths and words and a direct connection with the Witt formula is round. (C) 1997 American Institute of Physics.38210141034