This chapter explains the notation for the basic construction of the correction. It employs the Einstein summation convention, according to which there is an implied summation when a pair of indices is repeated, and the conventions of abstract index notation, so that upper indices and lower indices distinguish contravariant and covariant tensors. It also presents the notation concerning multi-indices which will later prove helpful for expressing higher order derivatives of a composition. In this notation, a K-tuple of multi-indices is said to form an ordered K-partition of a multi-index if there is a partition whereby the subsets are pairwise disjoint and are ordered by their largest elements.
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