Revisiting The R\'edei-Berge Symmetric Functions via Matrix Algebra
Abstract
We revisit the R\'edei-Berge symmetric function UD for digraphs D, a specialization of Chow's path-cycle symmetric function. Through the lens of matrix algebra, we consolidate and expand on the work of Chow, Grinberg and Stanley, and Lass concerning the resolution of UD in the power sum and Schur bases. Along the way we also revisit various results on Hamiltonian paths in digraphs.
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