On algebraic structures of spatial ordering and location code

摘要

The methodology of spatial ordering has been widely applied to many computational paradigms. A spatial ordering is usually expressed as a location code. This paper tries to fill the gap on the algebraic structures of spatial ordering. Several theorems on existence of the linear location code are stated and proved. The quadrant-recursive orders are characterized with Kronecker algebra. The generalized linear code and binomial location code are introduced to represent most applicable spatial orders. The outstanding sparsity presented in their characteristic matrices may significantly improve the computability of concerned paradigms.