Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory
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 -...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2024 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2024
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212606 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory. Christian Krattenthaler. SIGMA 20 (2024), 089, 6 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862733335397138432 |
|---|---|
| author | Krattenthaler, Christian |
| author_facet | Krattenthaler, Christian |
| citation_txt | Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory. Christian Krattenthaler. SIGMA 20 (2024), 089, 6 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-21T18:24:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212606 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:24:38Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Krattenthaler, Christian 2026-02-09T08:05:27Z 2024 Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory. Christian Krattenthaler. SIGMA 20 (2024), 089, 6 pages 1815-0659 2020 Mathematics Subject Classification: 33D15; 05A30; 14J32; 14N35; 53D45; 57M27 arXiv:2102.02360 https://nasplib.isofts.kiev.ua/handle/123456789/212606 https://doi.org/10.3842/SIGMA.2024.089 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. I am indebted to the anonymous referees for their many extremely helpful comments, which not only led to an improved presentation but also let me discover a subtle gap in the proof of Proposition 3 in the original version of the manuscript. This research was partially supported by the Austrian Science Foundation FWF (grant S50-N15) in the framework of the Special Research Program “Algorithmic and Enumerative Combinatorics”. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory Article published earlier |
| spellingShingle | Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory Krattenthaler, Christian |
| title | Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory |
| title_full | Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory |
| title_fullStr | Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory |
| title_full_unstemmed | Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory |
| title_short | Proof of Two Multivariate -Binomial Sums Arising in Gromov-Witten Theory |
| title_sort | proof of two multivariate -binomial sums arising in gromov-witten theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212606 |
| work_keys_str_mv | AT krattenthalerchristian proofoftwomultivariatebinomialsumsarisingingromovwittentheory |