On minimal free resolutions of sub-permanents and other ideals arising in complexity theory Academic Article uri icon


  • © 2018 Elsevier Inc. We compute the linear strand of the minimal free resolution of the ideal generated by k×k sub-permanents of an n×n generic matrix and of the ideal generated by square-free monomials of degree k. The latter calculation gives the full minimal free resolution by [1]. Our motivation is to lay groundwork for the use of commutative algebra in algebraic complexity theory. We also compute several Hilbert functions relevant for complexity theory.

author list (cited authors)

  • Efremenko, K., Landsberg, J. M., Schenck, H., & Weyman, J.

citation count

  • 1

publication date

  • June 2018