Are There Elimination Algorithms for the Permanent?

Research output: Contribution to journalArticle

Abstract

We define the class of elimination algorithms. There are algebraic algorithms for evaluating multivariate polynomials, and include as a special case Gaussian elimination for evaluating the determinant. We show polynomials, and include as a special case Gaussian elimination for evaluating the determinant. We show how to find the linear symmetries of a polynomial, defined appropriately, and use these methods to find the linear symmetries of the permanent and determinant. We show that in contrast to the Gaussian elimination algorithm for the determinant, there is no elimination algorithm for the permanent.

Original languageEnglish (US)
Pages (from-to)145-162
Number of pages18
JournalLinear and Multilinear Algebra
Volume33
Issue number3-4
DOIs
StatePublished - Dec 1 1992

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