Two general kinds of subsets of a partially ordered set P are always retracts of P:: (1) every maximal chain of P is a retract; (2) in P, every isometric, spanning subset of length one with no crowns is a retract. It follows that in a partially ordered set P with the fixed point property, every maxi
From a connected, partially ordered set of events to a partially ordered field of time intervals
✍ Scribed by P. G. Vroegindewey; V. Ja. Kreinovič; O. M. Kosheleva
- Publisher
- Springer US
- Year
- 1980
- Tongue
- English
- Weight
- 952 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0015-9018
No coin nor oath required. For personal study only.
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For a graph G whose vertices are vl, u2, . . . , v, and where E is the set of edges, we define a functional U,(h)= ss SC . . . frl,$EEh(Xi,Xj) > dPc(x~)dAxJ ... dp(x,), where h is a nonnegative symmetric function of two variables. We consider a binary relation + for graphs with fixed numbers of vert
## Behrendt, G., The lattice of antichain cutsets of a partially ordered set, Discrete Mathematics 89 (1991) 201-202. Every finite lattice is isomorphic to the lattice of antichain cutsets of a finite partially ordered set whose chains have at most three elements. A subset A of a partially order