We consider the order dimension of suborders of the Boolean lattice Bn. In particular we show that the suborder consisting of the middle two levels of Bn dimension at most of 6 log3n. More generally, we show that the suborder consisting of levels s and s+k of Bn has dimension O(k2 log n).
- Bollean lattice
- Mathematics Subject Classifications (1991): 06A07, 05C35
- Ordered set
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology
- Computational Theory and Mathematics