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Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>2 ['A',2]=>7 ['B',2]=>9 ['G',2]=>13 ['A',3]=>66 ['B',3]=>209 ['C',3]=>209 ['A',4]=>3061 ['B',4]=>103484 ['C',4]=>103484 ['D',4]=>9719 ['F',4]=>9593133 ['A',5]=>1095266
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Description
The number of reduced decompositions of the Weyl Group of the given Cartan type.
Equivalently, the number of chains based at the identity in the weak order.
References
[1] Total number of reduced decompositions for all permutations in S_n. OEIS:A246865
[2] The number of reduced decompositions of the longest element of the Weyl group of the given Cartan type. St001585
[3] The number of reduced words for a permutation. St000001
[4] The number of reduced words of a signed permutation. St001768
Code
def statistic(c):
    return sum(1 for e in WeylGroup(c) for _ in e.reduced_words_iter())
Created
Nov 18, 2025 at 08:57 by Martin Rubey
Updated
Nov 18, 2025 at 13:03 by Scott Neville