Retracts of partially ordered sets
- 1 March 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 27 (4) , 495-506
- https://doi.org/10.1017/s1446788700013483
Abstract
Let P be a finite, connected partially ordered set containing no crowns and let Q be a subset of P. Then the following conditions are equivalent: (1) Q is a retract of P; (2) Q is the set of fixed points of an order-preserving mapping of P to P; (3) Q is obtained from P by dismantling by irreducibles.Keywords
This publication has 3 references indexed in Scilit:
- A fixed point theorem for finite partially ordered setsJournal of Combinatorial Theory, Series A, 1976
- Crowns, Fences, and Dismantlable LatticesCanadian Journal of Mathematics, 1974
- Rings of setsDuke Mathematical Journal, 1937