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On minimal free resolutions of sub-permanents and other ideals arising in complexity theory (1504.05171v3)
Published 20 Apr 2015 in cs.CC, math.AC, and math.AG
Abstract: We compute the linear strand of the minimal free resolution of the ideal generated by k x k sub-permanents of an n x 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 work of Biagioli-Faridi-Rosas. 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.