TY - JOUR

T1 - Are There Elimination Algorithms for the Permanent?

AU - Sturtivant, Carl

PY - 1992/12/1

Y1 - 1992/12/1

N2 - 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.

AB - 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.

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U2 - 10.1080/03081089308818189

DO - 10.1080/03081089308818189

M3 - Article

AN - SCOPUS:84949695703

VL - 33

SP - 145

EP - 162

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 3-4

ER -