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math.CO2025
Eigenvalues of Universal Covers and the Matching Polynomial
Thomás Jung Spier
In this work, we prove that the universal and maximal abelian covers of a finite multi-graph have the same eigenvalues. This result strengthens a recent theorem of Li, Magee, Sabri…
quant-ph2025
Orthogonal polynomials, quantum walks and the Prouhet-Tarry-Escott problem
Frederico Cançado, Gabriel Coutinho, Thomás Jung Spier
This paper is motivated by the following problem. Define a quantum walk on a positively weighted path (linear chain). Can the weights be tuned so that perfect state transfer occurs…
math.CO2025
Efficient reconstruction of the characteristic polynomial
Thomás Jung Spier
The polynomial reconstruction problem, introduced by Cvetković in 1973, asks whether the characteristic polynomial of a graph with at least vertices can be reconstruc…