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<p>An elementary proof of quadratic lower bound for determinantal complexity of the permanent in positive characteristic is stated. This is achieved by constructing a sequence of matrices with zero permanent, but the rank of Hessian is bounded below by a degree two polynomial.</p>

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Degree 2 Lower Bound for Permanent in Arbitrary Characteristic

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • Harpreet Bedi,
  • Jason Suagee

摘要

An elementary proof of quadratic lower bound for determinantal complexity of the permanent in positive characteristic is stated. This is achieved by constructing a sequence of matrices with zero permanent, but the rank of Hessian is bounded below by a degree two polynomial.