Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffians

Sergio Caracciolo, Alan D. Sokal, Andrea Sportiello

The classic Cayley identity states that \det(\partial) (\det X)^s = s(s+1)...(s+n-1) (\det X)^{s-1} where X=(x_{ij}) is an n-by-n matrix of indeterminates and \partial=(\partial/\p…