Partial Transpose of Permutation Matrices
نویسندگان
چکیده
The main purpose of this paper is to look at the notion of partial transpose from the combinatorial side. In this perspective, we solve some basic enumeration problems involving partial transpose of permutation matrices. Specifically, we count the number of permutations matrices which are invariant under partial transpose. We count the number of permutation matrices which are still permutation matrices after partial transpose. We solve this problem also for transpositions. In this case, there is little evidence to justify a link between some permutations, partial transpose, and certain domino tilings. Qing-Hu Hou, Toufik Mansour, and Simone Severini Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China Department of Mathematics, University of Haifa, Haifa 31905, Israel Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Canada [email protected], [email protected], [email protected]
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Partial Transposes of Permutation Matrices
The partial transpose of a block matrix M is the matrix obtained by transposing the blocks of M independently. We approach the notion of the 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 invarian...
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