Caracciolo, S;
Sokal, AD;
Sportiello, A;
(2013)
Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffians.
Advances in Applied Mathematics
, 50
(4)
pp. 474-594.
10.1016/j.aam.2012.12.001.
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Abstract
The classic Cayley identity states that where is an matrix of indeterminates and is the corresponding matrix of partial derivatives. In this paper we present straightforward algebraic/combinatorial proofs of a variety of Cayley-type identities, both old and new. The most powerful of these proofs employ Grassmann algebra (= exterior algebra) and Grassmann–Berezin integration. Among the new identities proven here are a pair of “diagonal-parametrized” Cayley identities, a pair of “Laplacian-parametrized” Cayley identities, and the “product-parametrized” and “border-parametrized” rectangular Cayley identities.
| Type: | Article |
|---|---|
| Title: | Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffians |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.aam.2012.12.001 |
| Publisher version: | https://doi.org/10.1016/j.aam.2012.12.001 |
| Language: | English |
| Additional information: | This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10101899 |
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