Linear Inequalities for Rank 3 Geometric Lattices

Kathryn L. Nyman
2004 Discrete & Computational Geometry  
The flag Whitney numbers (also referred to as the flag f -numbers) of a geometric lattice count the number of chains of the lattice with elements having specified ranks. We give a collection of inequalities which imply all the linear inequalities satisfied by the flag Whitney numbers of rank 3 geometric lattices. We further describe the smallest closed convex set containing the flag Whitney numbers of rank 3 geometric lattices as well as the smallest closed convex set containing the flag
more » ... numbers of those lattices corresponding to oriented matroids.
doi:10.1007/s00454-003-0807-6 fatcat:5patoufjobdevgie73lnbg3e3e