On a Class of Subspace Lattices
Received:February 23, 1997  
Key Words: poset   subspace lattice   Sperner property   q   analog.  
Fund Project:
Author NameAffiliation
Wang Yi Dept. of Math.
Dalian University of
Dalian 116024 
Hits: 1946
Download times: 1378
      Let Vn(q) be the n-dimensional vector space over the finite field with q elements and Ln(q) denote the lattice of subspaces of Vn(q). Let , K a k-dimensional subspace and C[n,k] the set of the subspaces S such that S∩K≠=O. We show that C[n,k] is Sperner and unimodal and point out all maximum-sized antichains in C[n,k]. For the Whitney number Wm of C[n,k], we show that Wm2-qWm-1Wm+1 has nonnegative coefficients as a polynomial in q and that W0≤Wn≤W1≤Wn-1≤W2≤….
View Full Text  View/Add Comment  Download reader