Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory
arXiv:2102.02360 · doi:10.3842/SIGMA.2024.089
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-Saalschütz summation formula from the theory of basic hypergeometric series.