Geodesic
Revisiting The Rédei-Berge Symmetric Functions via Matrix Algebra
John Irving1 ; Mohamed Omar2
1Saint Mary's University, Halifax, Nova Scotia, Canada
2York University
The electronic journal of combinatorics, Tome 32 (2025) no. 4
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We revisit the Rédei-Berge symmetric function $\mathcal{U}_D$ 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 $\mathcal{U}_D$ in the power sum and Schur bases. Along the way we also revisit various results on Hamiltonian paths in digraphs.
DOI : 10.37236/13841

John Irving  1   ; Mohamed Omar  2

1 Saint Mary's University, Halifax, Nova Scotia, Canada
2 York University 
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     title = {Revisiting {The} {R\'edei-Berge} {Symmetric} {Functions} via {Matrix} {Algebra}},
     journal = {The electronic journal of combinatorics},
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     number = {4},
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John Irving; Mohamed Omar. Revisiting The Rédei-Berge Symmetric Functions via Matrix Algebra. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13841

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