representation theory

Big data approach to Kazhdan-Lusztig polynomials

arXiv:2412.01283 · doi:10.56994/JXM.002.001.002

summary

The paper uses large‑scale computational and data‑analysis techniques to study Kazhdan‑Lusztig polynomials for symmetric groups up to size 11, revealing structural patterns through exploratory and topological data analysis.

Abstract

We investigate the structure of Kazhdan-Lusztig polynomials of the symmetric group by leveraging computational approaches from big data, including exploratory and topological data analysis, applied to the polynomials for symmetric groups of up to 11 strands.

27 pages, many figures, comments welcome, appeared in J. Exp. Math, added a remark acknowledging E. O. Hjelle for proposing an AI-generated proof of Conjecture 6.4 (via ChatGPT 5.5 Pro), added a link to the complete proof on our GitHub repository

Topics & keywords

#kazhdan-lusztig polynomials#symmetric group#big data analysis#topological data analysis#computational algebraKazhdan-Lusztig polynomialssymmetric group S_nbig data methodsexploratory data analysistopological data analysiscomputational experiments
Big data approach to Kazhdan-Lusztig polynomials · wovepaper