Mathematics > Combinatorics
arXiv:1606.08193 (math)
[Submitted on 27 Jun 2016 (v1), last revised 16 Jun 2026 (this version, v2)]
Abstract:We show a determinant identity which generalizes both the Chio pivotal condensation theorem and the Matrix-Tree theorem.
| Comments: | 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" |
| Subjects: | Combinatorics (math.CO) |
| MSC classes: | 05C50, 15A15 |
| Cite as: | arXiv:1606.08193 [math.CO] |
| (or arXiv:1606.08193v2 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.1606.08193 arXiv-issued DOI via DataCite |
Submission history
From: Darij Grinberg [view email]
[v1]
Mon, 27 Jun 2016 10:14:52 UTC (20 KB)
[v2]
Tue, 16 Jun 2026 06:14:21 UTC (216 KB)
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Code, Data, Media
Code, Data and Media Associated with this Article
Demos
Demos
Related Papers
Recommenders and Search Tools
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.




















