Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs
Quantum Algebra
2009-11-11 v1 Combinatorics
Abstract
To directed graphs with unique sink and source we associate a noncommutative associative alsgebra and a polynomial over this algebra. Edges of the graph correspond to pseudo-roots of the polynomial. We give a sufficient condition when coefficients of the polynomial can be rationally expressed via elements of a given set of pseudo-roots (edges). Our results are based on a new theorem for directed graphs also proved in this paper.
Keywords
Cite
@article{arxiv.math/0509260,
title = {Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs},
author = {Israel Gelfand and Sergei Gelfand and Vladimir Retakh and Robert Lee Wilson},
journal= {arXiv preprint arXiv:math/0509260},
year = {2009}
}
Comments
15 pages, AMSTeX