Non-unique factorizations, land surveying and electricity

Details Non-unique factorizations, land surveying and electricity Non-unique factorizations, land surveying and electricity

2010-02-15

arxiv.org/abs/1002.2905v3

Mathematics

Combinatorics

11 pages, first in a series

Scientific paper

Non-unique factorizations theory, which started in algebraic number theory, over the years has expanded into several areas of mathematics. Here, we propose yet another branching. We show that some concepts of factorizations theory, such as half factorial and weak half factorial properties can be translated via Cayley graphs into graph theory. It is proved, that subset S of abelian group G is half factorial, if and only if the Cayley digraph Cay(G; S) is geodetical, e.g., simple paths connecting a fixed pair of vertices have the same length. Further, it is shown that the voltage digraph naturally arising from subset S of group G satisfies Kirchoff's Voltage Law exactly when S is weakly half factorial. In the concluding remarks, some loosely formulated ideas for further research are presented..

Affiliated with

Also associated with

No associations

Rating

Non-unique factorizations, land surveying and electricity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-unique factorizations, land surveying and electricity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-unique factorizations, land surveying and electricity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-146292