Proof of Two Multivariate $q$-Binomial Sums Arising in Gromov-Witten Theory
Classical Analysis and ODEs
2024-10-11 v3 Algebraic Geometry
Combinatorics
Abstract
We prove two multivariate -binomial identities conjectured by Bousseau, Brini and van Garrel [Geom. Topol. 28 (2024), 393-496, arXiv:2011.08830] which give generating series for Gromov-Witten invariants of two specific log Calabi-Yau surfaces. The key identity in all the proofs is Jackson's -analogue of the Pfaff-Saalsch\"utz summation formula from the theory of basic hypergeometric series.
Keywords
Cite
@article{arxiv.2102.02360,
title = {Proof of Two Multivariate $q$-Binomial Sums Arising in Gromov-Witten Theory},
author = {Christian Krattenthaler},
journal= {arXiv preprint arXiv:2102.02360},
year = {2024}
}