Article ID Journal Published Year Pages File Type
4656536 Journal of Combinatorial Theory, Series A 2006 19 Pages PDF
Abstract

In this paper, we solve the conjecture about the combinatorial invariance of Kazhdan–Lusztig polynomials for the first open cases, showing that it is true for intervals of length 5 and 6 in the symmetric group. We also obtain explicit formulas for the R-polynomials and for the Kazhdan–Lusztig polynomials associated with any interval of length 5 in any Coxeter group, showing in particular what they look like in the symmetric group.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics