On minimal free resolutions of sub-permanents and other ideals arising in complexity theory

Klim Efremenko, J. M. Landsberg, Hal Schenck, Jerzy Weyman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)8-20
Number of pages13
JournalJournal of Algebra
Volume503
DOIs
StatePublished - 1 Jun 2018

Keywords

  • Computational complexity
  • Determinant
  • Free resolution
  • Permanent

ASJC Scopus subject areas

  • Algebra and Number Theory

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