Maximal antichains under dimension constraints

✍ Scribed by R. Ahlswede; H. Aydinian; L.H. Khachatrian

• Book ID: 104113305
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 202 KB
• Volume: 273
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(03)00226-7

✦ Synopsis

We consider A(n; k) = max A {|A| : dim(A) 6 k, A ⊂ {0; 1} n is an antichain}, where the dimension is taken from the linear span of A in R n , we conjecture the exact value of A(n; k) and we prove this conjecture for all n and k 6 n=2 + 1 or k = n -1. This is a contribution to the program of systematic investigation of extremal problems under dimension constraints, which was recently presented by the authors.