Derivation of low-temperature series expansions for the Ising model with triplet interactions on the plane triangular lattice

The derivation of low-temperature (high-field) series expansions for the Ising model with pure triplet interactions on the plane triangular lattice is described. Euler's law of the edges is used to transform the linkage rule into a form convenient for the derivation of ferromagnetic polynomials. Explicit results are given for the ferromagnetic polynomials corresponding to the first twelve powers of the temperature variable (u 3 ) both as functions of the field variable ( mu ) and, in zero field, as functions of the temperature variable (u 2 ) of the simple Ising model.