Partitions in Cartesian systems

On Extremal Set Partitions in Cartesian Product Spaces

Non-Cartesian Systems : an Open Problem

The following open problem is presented and motivated : Are there physical systems whose state spaces do not compose according to either the Cartesian product, as classical systems do, or the usual tensor product, as quantum systems do ? ”History is written with the feet ...”

k-Efficient partitions of graphs

A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...

Hyperplane partitions and difference systems of sets

Difference Systems of Sets (DSS) are combinatorial configurations that arise in connection with code synchronization. This paper gives new constructions of DSS obtained from partitions of hyperplanes in a finite projective space, as well as DSS obtained from balanced generalized weighing matrices and partitions of the complement of a hyperplane in a finite projective space. ∗Research supported ...

The logic of systems of granular partitions

The theory of granular partitions is designed to capture in a formal framework important aspects of the selective character of common-sense views of reality. It comprehends not merely the ways in which we can view reality by conceiving its objects as gathered together not merely into sets, but also into wholes of various kinds, partitioned into parts at various levels of granularity. We here re...