  In the paper nonlinear transformations of the Jordan-Wigner (JW) type are
introduced in the form different from the ones known previously, for the
purpose of expressing multi-index Pauli operators in terms of multi-index Fermi
creation and annihilation operators. These JW transformations in the general
case being a subject of a rather complicated algebra of transposition relations
between various sets of Fermi creation and annihilation operators, depending on
the common multiindex of the latter, is shown. As an example, the two- and
three- dimensional transformations of the JW type are investigated, their
properties and possible applications in analysis of a couple of lattice models
of statistical mechanics and also an example of application of these
transformations to problems of self-avoiding walks in graph theory, are
discussed. The relation of the obtained transformations to the previously known
transformations of the JW type for higher dimensions is shown.
