Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  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.  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.
['Federico Incitti']
I am writing a research paper on a idea On the combinatorial invariance of Kazhdan-Lusztig polynomials
[{"from": "human", "value": "I am writing a research paper on a idea On the combinatorial invariance of Kazhdan-Lusztig polynomials"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  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.  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."}]