Complexity and Completeness of Immanants
Abstract
Immanants are polynomial functions of n by n matrices attached to irreducible characters of the symmetric group S_n, or equivalently to Young diagrams of size n. Immanants include determinants and permanents as extreme cases. Valiant proved that computation of permanents is a complete problem in his algebraic model of NP theory, i.e., it is VNP-complete. We prove that computation of immanants is VNP-complete if the immanants are attached to a family of diagrams whose separation is for some . We define the separation of a diagram to be the largest number of overhanging boxes contained in a single row. Our theorem proves a conjecture of Buergisser for a large variety of families, and in particular we recover with new proofs his VNP-completeness results for hooks and rectangles.
Cite
@article{arxiv.cs/0301024,
title = {Complexity and Completeness of Immanants},
author = {Jean-Luc Brylinski and Ranee Brylinski},
journal= {arXiv preprint arXiv:cs/0301024},
year = {2007}
}
Comments
10 pages, Latex