**Identifier**

Identifier

Values

['A',9]
=>
5

['A',10]
=>
28

['A',1]
=>
1

['A',2]
=>
1

['B',2]
=>
1

['G',2]
=>
1

['A',3]
=>
1

['B',3]
=>
1

['C',3]
=>
1

['A',4]
=>
1

['B',4]
=>
1

['C',4]
=>
1

['D',4]
=>
1

['F',4]
=>
1

['A',5]
=>
1

['B',5]
=>
2

['C',5]
=>
2

['D',5]
=>
1

['A',6]
=>
1

['A',7]
=>
1

['A',8]
=>
1

Description

The largest mu-coefficient of the Kazhdan Lusztig polynomial occurring in the Weyl group of given type.

The $\mu$-coefficient of the Kazhdan-Lusztig polynomial $P_{u,w}(q)$ is the coefficient of $q^{\frac{l(w)-l(u)-1}{2}}$ in $P_{u,w}(q)$.

The $\mu$-coefficient of the Kazhdan-Lusztig polynomial $P_{u,w}(q)$ is the coefficient of $q^{\frac{l(w)-l(u)-1}{2}}$ in $P_{u,w}(q)$.

References

[1]

**Warrington, G. S.***Equivalence classes for the ยต-coefficient of Kazhdan-Lusztig polynomials in $S_n$*MathSciNet:2859901Code

def statistic(C): W = CoxeterGroup(C, implementation='coxeter3') r = [] for u in W: U = (W(v) for v in W.bruhat_interval(u, W.long_element())) next(U) for v in U: ldiff = v.length()-u.length()-1 if is_even(ldiff): p = W.kazhdan_lusztig_polynomial(u, v) r.append(p[ldiff//2]) return max(r)

Created

Apr 18, 2018 at 22:49 by

**Martin Rubey**Updated

Apr 18, 2018 at 22:49 by

**Martin Rubey**searching the database

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