Intersecting antichains and shadows in linear lattices

Authors:
Jun Wang
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, PR China
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

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Abstract

We establish a homomorphism of finite linear lattices onto the Boolean lattices via a group acting on linear lattices. By using this homomorphism we prove the intersecting antichains in finite linear lattices satisfy an LYM-type inequality, as conjectured by Erdos, Faigle and Kern, and we state a Kruskal-Katona type theorem for the linear lattices.