Elementary Atoms, Positive Bases and Reay Systems

Abstract

The chapter begins with some basic non-degeneracy characterizations. The concept of an elementary atom is given. It corresponds to the notion of atom when factoring using rational sequences rather than ordinary sequences. A version of Carathéordory’s Theorem, formulated for rational sequences, is given. Positive bases are introduced, with a lengthy list of equivalent defining conditions, including equivalent formulations involving elementary atoms. The notion of a Reay system and related concepts are introduced, and the basic theory of positive bases extended to this context. The section concludes with the technical stability properties of complete simplicial fans.

Publication Title

Lecture Notes in Mathematics

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