Space and Particles

Elements in the strong ring within the Stanley-Reisner ring still can be seen as geometric objects for which mathematical theorems known in topology hold. But there is also arithemetic. We remark that the multiplicative primes in the ring are the simplicial complexes. The Sabidussi theorem imlies that additive primes (particles) have a unique prime factorization (into elementary particles).

One ring to rule them all

Arithmetic with networks The paper “On the arithmetic of graphs” is posted. (An updated PDF). The paper is far from polished, the document already started to become more convoluted as more and more results were coming in. There had been some disappointment early June when realizing that the Zykov multiplication (which I had been proud of discovering in early January) … ….