Name
Abstract | ||
|---|---|---|
Let M be a family of sequences (a1,..., ap) where each ak is a flat in a projective geometry of rank n (dimension n- 1) and order q, and the sum of ranks, r(a1)+ ... + r(ap), equals the rank of the join a1 ∨ ... ∨ ap. We prove upper bounds on |M| and corresponding LYM inequalities assuming that (i) all joins are the whole geometry and for each k the set of all ak's of sequences in M contains no chain of length l, and that (ii) the joins are arbitrary and the chain condition holds for all k. These results are q-analogs of generalizations of Meshalkin's and Erdös's generalizations of Sperner's theorem and their LYM companions, and they generalize Rota and Harper's q-analog of Erdös's generalization. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0097-3165(03)00049-9 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
primary 05d05,rank n,meshalkin's theorem,r -chain-free,sperner's theorem,r -family,chain condition,length l,upper bound,dimension n,lym companion,lym inequality,order q,projective geometry,secondary 06a07,corresponding lym inequality,antichain,whole geometry,51e20,meshalkin theorem,projective geometries | Discrete mathematics,Combinatorics,Antichain,Joins,Sperner's theorem,Projective geometry,Generalization,Mathematics,Projective test | Journal |
Volume | Issue | ISSN |
102 | 2 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
1 | 2.40 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Matthias Beck | 1 | 34 | 8.39 |
| T. Zaslavsky | 2 | 297 | 56.67 |