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
Semigroups of order preserving partial transformations of a totally ordered set
β Scribed by N.R Reilly
- Publisher
- Elsevier Science
- Year
- 1972
- Tongue
- English
- Weight
- 1015 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0021-8693
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π SIMILAR VOLUMES
The closed cone of flag vectors of Eulerian partially ordered sets is studied. A new family of linear inequalities valid for Eulerian flag vectors is given. Half-Eulerian posets are defined. Certain limit posets of Billera and Hetyei are half-Eulerian; they give rise to extreme rays of the cone for
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