2005/08/05 by Ilda P. F. Da Silva, Da Silva, Ilda P. F.
Mathematics · #05B35 #52C40 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.CO #math.MG #msc:05B35 #msc:52C40
paper · pdf · doi:10.48550/arxiv.math/0508103
17pp
arxiv created 2005/08/05 · arxiv updated 2009/12/01
Las Vergnas Cube Conjecture states that the cube matroid has exactly one class of orientations. We prove that this conjecture is equivalent to saying that the oriented matroid of the affine dependencies of the n-cube can be reconstructed from the underlying matroid and one of the following partial lists of signed circuits or cocircuits: A) the signed circuits of rank 3, or B) the positive signed cocircuits.