From Chio Pivotal Condensation to the Matrix-Tree theorem
arXiv:1606.08193
Abstract
We show a determinant identity which generalizes both the Chio pivotal condensation theorem and the Matrix-Tree theorem.
32 pages; comments are welcome. v2 corrects errors found by GPT-5.5 and updates links. The ancillary file is a short expository note "Combinatorial proof of Chio Pivotal Condensation"