Tensor compositions and lists of combinatorial structures

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Abstract
By a list B we mean a finite linearly ordered set. Let be a sublist and let V denote a vector space isomorphic to the free vector space generated by B over a field F of characteristic zero. Assume the isomorphism is explicitly given by a function Let S be a distinguished subset of V and let Q be a finite set. A function will be called an S-composition of L if . Various compositions of a list provide alternative ways of generating, storing, and manipulating the list in machine computation. In this paper we study some of the properties of such compositions in the case where B = RD is a finite function spaceV is an algebra of tensors, and S certain distinguished subsets of V such as the homogeneous tensors. The problem of generating compositions of lists of orbit classes of L under group actions is also considered.

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