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Partial transpose of permutation matrices

Hou, QH; Mansour, T; Severini, S; (2007) Partial transpose of permutation matrices.

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Abstract

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.

Type:Article
Title:Partial transpose of permutation matrices
Additional information:13 pages
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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