Open Research Index

The Cauchy–Binet formula, Kirchhoff's matrix-tree theorem and Cayley's formula

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-16-000019Oct 16, 2026math.COscore 0

A Lean 4 / Mathlib formalization of the Cauchy–Binet formula for determinants of products of rectangular matrices over commutative rings (not in Mathlib), of Kirchhoff's matrix-tree theorem (the number of spanning trees of a finite graph is any principal cofactor of Mathlib's Laplacian matrix), and of Cayley's formula (n^(n−2) labelled trees on n ≥ 1 vertices), derived from the matrix-tree theorem for the complete graph.

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