What does this research mean for the field?

In finite free-boundary honeycomb domains, the logarithm of the number of spanning trees decomposes into a bulk entropy coefficient of approximately 0.807735, a geometry-stable boundary coefficient of approximately -0.662, and a subleading logarithmic term that correlates with polygonal corner structure. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Determine how the total count of spanning trees decomposes into bulk, boundary, and corner contributions across finite honeycomb lattice domains with free boundaries.

September 5, 2026Open Access

Finite-Size Structure of Spanning Trees on Free-Boundary Honeycomb Domains: Bulk, Boundary and Corner Contributions

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Authors

JVJulio Cesar Santana Valderrama Santana Valderrama

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Implication

Computational study reveals bulk, boundary, and corner scaling of spanning trees on honeycomb domains, indicating distinct lattice and geometric contributions.

Key Points

Determine how the total count of spanning trees decomposes into bulk, boundary, and corner contributions across finite honeycomb lattice domains with free boundaries.
Evaluated spanning tree counts across hexagonal, rhombic, and triangular domains using exact integer determinants for small systems and Laplacian eigenvalue spectra for larger graphs.
Applied local-difference extrapolation to isolate the boundary coefficient while reducing fitting collinearity.
Constructed numerical irreducible-representation projection operators to verify the dihedral D6 symmetry of hexagonal domain spectra.
Obtained a leading bulk entropy coefficient of h ≈ 0.807735 and a geometry-stable boundary coefficient of a ≈ -0.662 across all three domain families.
Identified an empirical linear relationship for the subleading logarithmic corner coefficient, b ≈ 0.133 S + 0.562 with R² ≈ 0.991, across polygonal corner descriptors.
Demonstrated exact D6 symmetry constraints with reconstruction errors near 10^-14, explaining paired eigenvalue degeneracies via two-dimensional irreducible sectors.

Cite This Study

Julio Cesar Santana Valderrama Santana Valderrama (2026) studied this question.

synapsesocial.com/papers/6a9bd48c6b95aff0620ec420 https://doi.org/10.5281/zenodo.22282116

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Implication

Computational study reveals bulk, boundary, and corner scaling of spanning trees on honeycomb domains, indicating distinct lattice and geometric contributions.

Finite-Size Structure of Spanning Trees on Free-Boundary Honeycomb Domains: Bulk, Boundary and Corner Contributions

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Key Points

Cite This Study

Finite-Size Structure of Spanning Trees on Free-Boundary Honeycomb Domains: Bulk, Boundary and Corner Contributions

Discussion

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Implication

Key Points

Cite This Study

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