The antipodal layers problem

✍ Scribed by Glenn Hurlbert

• Book ID: 103061190
• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 481 KB
• Volume: 128
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)90115-5

✦ Synopsis

For n > 2k and [n] = { 1,2, . . , n}, let the bipartite graph 4,t have vertices {A c [n] 1) A I= k or n-k) and edges {(A, B)j A c B}. It has been conjectured that Ask+ I,t (the middle two levels of the Boolean lattice .!!2z"f') is Hamiltonian, and we conjecture the same for arbitrary n. Here we show that the conjecture holds for n bigger than roughly k', with k large enough. We also define a new product between ranked posets, giving rise to many new representations of _&+ l.lr.