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novou/square-maximality-palomar

Jiechen Zhang

Palomar Registrypalomar/PALOMAR-2026-08-23-000003Aug 23, 2026math.COscore 0

A Lean 4 formalization of square maximality for spanning trees of induced subgraphs of the square lattice. For every positive integer n and every finite set S of n^2 points in Z^2, the induced lattice graph on S has at most as many spanning trees as the n by n square, with equality exactly when S is a translate of that square. The development also proves the corresponding strict and equality statements for arbitrary spanning subgraphs, together with the finite Matrix--Tree theorem and the proof chain used by the paper.

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