1. Introduction. The Lagrange inversion formula is one of the fundamental results of enumerative combinatorics. It expresses the coefficients of powers of the compositional inverse of a power series in terms of the coefficients of powers of the original power series. G. Labelle [10] extended Lagrange inversion to cycle index series, which are equivalent to symmetric functions. Although motivate...

We investigate the stationarity of variational integrals evaluated on solutions a system differential equations. First, fundamental concepts are relieved accidental structures and hypothetical assumptions. The constraints