2
votes
1answer
90 views

Example involving partially ordered Abelian groups

Definition 1: Let $(G,\leq)$ be a nonzero partially ordered Abelian group with order unit $u$. (Recall that $u\in G$ is a order unit if, for every $g\in G$, there exists $N\in\mathbb N$ such that ...
2
votes
1answer
256 views

Is there a Dirichlet Unitary Unit Theorem?

Dirichlet's unit theorem computes the group of units of the algebraic numbers of a number field. There are a few generalisations for orders available. Assume the order has an involution. For example, ...
10
votes
1answer
757 views

Discrete version of Nullstellensatz?

Hi. I was reading the paper "On the foundations of combinatorial theory (VI): The idea of a generating function" by Doubilet, Rota and Stanley, and there is a relation treated which is very ...
7
votes
1answer
2k views

Number of graphs with a given number of nodes, edges and triangles

Hi. Does anyone know if it is possible to enumerate the set of labeled/unlabeled graphs (loopless, undirected, only one edge between pairs of nodes) having a given number of nodes, edges and ...