Finite three dimensional partial orders which are not sphere orders

Finite Three Dimensional Partial Orderswhich Are Not Sphere

Given a partially ordered set P = (X; P), a function F which assigns to each x 2 X a set F (x) so that x y in P if and only if F (x) F (y) is called an inclusion representation. Every poset has such a representation, so it is natural to consider restrictions on the nature of the images of the function F. In this paper, we consider inclusion representations assigning to each x 2 X a sphere in R ...

Extending Partial Orders to Dense Linear Orders

Partial Orders on Partial Isometries

This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spac...

Computably Enumerable Partial Orders

We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enumerable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for such orders, and show that the latter is strictly stronger than the latter. We then show that every ∅′-computable structure (or even just of c.e. degree) has ...

Mutually complementary partial orders

Two partial orders P = (X, S) and Q = (X, s’) are complementary if P fl Q = {(x, x): x E x} and the transitive closure of P U Q is {(x. y): x, y E X}. We investigate here the size w(n) of the largest set of pairwise complementary par!iai orders on a set of size n. In particular, for large n we construct L?(n/iogrt) mutually complementary partial orders of order n, and show on the other hand tha...