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Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs

Israel Gelfand·Sergei Gelfand·Vladimir Retakh·Robert Lee Wilson
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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.

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Israel Gelfand, Sergei Gelfand, Vladimir Retakh, Robert Lee Wilson. 2005-09-12. Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs. https://doi.org/10.1007/s11005-005-0024-8

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