Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory - Krattenthaler, Christian (Symmetry, Integrability and Geometry: Methods and Applications, 2024)
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.