Big data approach to Kazhdan-Lusztig polynomials

TL;DR

This paper applies big data techniques, such as exploratory and topological data analysis, to study Kazhdan-Lusztig polynomials of symmetric groups up to 11 strands, revealing new structural insights.

Contribution

It introduces a novel computational approach combining big data methods with algebraic combinatorics to analyze Kazhdan-Lusztig polynomials.

Findings

Identifies structural patterns in Kazhdan-Lusztig polynomials for symmetric groups up to 11 strands.

Demonstrates the effectiveness of big data techniques in algebraic combinatorics.

Provides a foundation for further computational exploration of algebraic structures.

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.