The computational complexity of immanants

被引：0
|
作者：
Bürgisser, P. [1 ]
机构：
[1] Dept. of Math. and Computer Science, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
来源：
| 2001年 / Society for Industrial and Applied Mathematics Publications卷 / 30期
关键词：
Algorithms - Mathematical models - Matrix algebra - Polynomials - Turing machines;
D O I：
10.1137/S0097539798367880
中图分类号：
学科分类号：
摘要：
Permanents and determinants are special cases of immanants. The latter are polynomial matrix functions defined in terms of characters of symmetric groups and corresponding to Young diagrams. Valiant has proved that the evaluation of permanents is a complete problem in both the Turing machine model (#P-completeness) as well as in his algebraic model (VNP-completeness). We show that the evaluation of immanants corresponding to hook diagrams or rectangular diagrams of polynomially growing width is both #P-complete and VNP-complete.
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