Dennis M. Combinatorial proofs of linear algebraic identities

Dartmouth: Dartmouth College, 2019. — 99 p.Basic Definitions
History
Lewis Carroll Identity
Dodgson/Muir Identity
The Matrix Tree Theorem
Involution Principle
Lewis Carroll and the Red Hot Potato
Connecting Identities
The Red Hot Potato algorithm
Sets
Involutions
Example
Proof of φ1
Identity Proofs
Connection to Zeilberger
Zeilberger’s Proof
Alternate Definition of φ1
Dodgson/Muir Identity
Connecting Identities
Generalized Red Hot Potato algorithm
Sets
Involutions
Generalized Red Hot Potato algorithm
Example
Proof that φ1 is a sign-reversing involution
Proofs of Forest and Lewis Carroll Identities
Future Work
Jacobi’s Theorem
Other Directions