Coplanarity of rooted spanning-tree vectors
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11005_2025_2026_ReferencePDF.pdf
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Author(s)
Polettini, Matteo
Harunari, Pedro E.
Cengio, Sara D.
Lecomte, Vivien
Date Issued
December 5, 2025
Journal
Letters in Mathematical Physics
Publisher
Springer Netherlands
Citation
Polettini, M., Harunari, P.E., Cengio, S.D. et al. Coplanarity of rooted spanning-tree vectors. Lett Math Phys 116, 1 (2026).
Version
Author's final manuscript
Abstract
Employing a recent technology of tree surgery, we prove a “deletion–constriction” formula for products of rooted spanning-trees on weighted directed graphs that generalizes deletion–contraction on undirected graphs. The formula implies that, letting τ x ∅ , τ x + , and τ x - be the rooted spanning-tree polynomials obtained, respectively, by removing both directed edges between two vertices, or by forcing the tree to pass through either edge, the vectors ( τ x ∅ , τ x + , τ x - ) are coplanar for all roots x . We deploy the result to give an alternative derivation of a recently found mutual linearity of stationary currents of Markov chains. We generalize deletion–constriction and current linearity for two pairs of edges and conjecture that similar results may hold for arbitrary subsets of edges.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s11005-025-02026-8
