On the linear classification of even and odd permutation matrices and the complexity of computing the permanent



The problem of linear classification of the parity of permutation matrices is studied. This problem is related to the analysis of complexity of a class of algorithms designed for computing the permanent of a matrix that generalizes the Kasteleyn algorithm. Exponential lower bounds on the magnitude of the coefficients of the functional that classifies the even and odd permutation matrices in the case of the field of real numbers and similar linear lower bounds on the rank of the classifying map for the case of the field of characteristic 2 are obtained.


permutation matrix parity permanent linear classification theta function independence number 


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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyDolgopudnyi, Moscow oblastRussia
  2. 2.Dorodnicyn Computing CenterFederal Research Center “Computer Science and Control,” Russian Academy of SciencesMoscowRussia

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