2007/09/21 by Qing-Hu Hou, Hou, Qing-Hu, Toufik Mansour +3
Engineering · Mathematics · Physics and Astronomy · #Graph theory and applications #Random Matrices and Applications #graph theory and CDMA systems #math.CO #quant-ph
paper · pdf · doi:10.48550/arxiv.0709.3547
13 pages
arxiv created 2008/03/22 · arxiv updated 2009/12/01
The partial transpose of a block matrix M is the matrix obtained by transposing the blocks of M independently. We approach the notion of partial transpose from a combinatorial point of view. In this perspective, we solve some basic enumeration problems concerning the partial transpose of permutation matrices. More specifically, we count the number of permutations matrices which are equal to their partial transpose and the number of permutation matrices whose partial transpose is still a permutation. We solve these problems also when restricted to symmetric permutation matrices only.