A short proof of a new combinatorial identity

Arkadij Bojko

Published 2021-11-18, updated 2021-12-22Version 3

While working with Grothendieck's Quot-schemes and their virtual enumerative invariants, the author came across a combinatorial identity which would have followed as a consequence of a very general abstract machinery. We dedicate this short note to give a combinatorial proof of this identity which is closely related to the Lagrange inversion. A special case of the result was proved by Mathoverflow users "Alex Gavrilov" and "esg" answering our enquiry.