Strings, tensorial combinants, and Bartlett adjustments

Abstract

The transformation laws for tensors, for affine connections and for derivatives of scalars may be subsumed under a general concept, termed a string. The intertwining of certain types of strings leads to new strings; thus intertwining of a symmetric scalar string and a symmetric connection string yields a sequence of symmetric tensors. Some statistical instances of strings are given and these are of use for representing various asymptotic expansions in invariant terms. As an example of this, invariant decompositions of Bartlett adjustments are briefly discussed.