MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

4 edited tags
3 added 16 characters in body

Let $P$ be a poset and denote by $Hom(P, \mathbb N)$ the set of all monotone functions from $P$ to natural numbers $\mathbb N$. Under what conditions on $P$ Is it possible to recover the order on $P$ from the knowledge of $Hom(P, \mathbb N)$?

I should mention here that the only example I am interested in is the poset of prime ideals in a commutative Noetherian ring.

It would be great if you could include references.

Thanks!

2 added 129 characters in body

Let $P$ be a poset and denote by $Hom(P, \mathbb N)$ the set of all monotone functions from $P$ to $\mathbb N$. Under what conditions on $P$ Is it possible to recover the order on $P$ from the knowledge of $Hom(P, \mathbb N)$?

I should mention here that the only example I am interested in is the poset of prime ideals in a commutative Noetherian ring.

It would be great if you could include references.

Thanks!

1