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Identifier
Values
=>
Cc0002;cc-rep
[]=>1 [1]=>1 [2]=>1 [1,1]=>1 [3]=>1 [2,1]=>4 [1,1,1]=>1 [4]=>1 [3,1]=>7 [2,2]=>4 [2,1,1]=>11 [1,1,1,1]=>1 [5]=>1 [4,1]=>11 [3,2]=>15 [3,1,1]=>32 [2,2,1]=>34 [2,1,1,1]=>26 [1,1,1,1,1]=>1 [6]=>1 [5,1]=>16 [4,2]=>26 [4,1,1]=>76 [3,3]=>15 [3,2,1]=>192 [3,1,1,1]=>122 [2,2,2]=>34 [2,2,1,1]=>180 [2,1,1,1,1]=>57 [1,1,1,1,1,1]=>1 [7]=>1 [6,1]=>22 [5,2]=>42 [5,1,1]=>156 [4,3]=>56 [4,2,1]=>474 [4,1,1,1]=>426 [3,3,1]=>267 [3,2,2]=>294 [3,2,1,1]=>1494 [3,1,1,1,1]=>423 [2,2,2,1]=>496 [2,2,1,1,1]=>768 [2,1,1,1,1,1]=>120 [1,1,1,1,1,1,1]=>1 [8]=>1 [7,1]=>29 [6,2]=>64 [6,1,1]=>288 [5,3]=>98 [5,2,1]=>1038 [5,1,1,1]=>1206 [4,4]=>56 [4,3,1]=>1344 [4,2,2]=>768 [4,2,1,1]=>5142 [4,1,1,1,1]=>2127 [3,3,2]=>855 [3,3,1,1]=>2829 [3,2,2,1]=>5946 [3,2,1,1,1]=>9204 [3,1,1,1,1,1]=>1389 [2,2,2,2]=>496 [2,2,2,1,1]=>4288 [2,2,1,1,1,1]=>2904 [2,1,1,1,1,1,1]=>247 [1,1,1,1,1,1,1,1]=>1 [9]=>1 [8,1]=>37 [7,2]=>93 [7,1,1]=>491 [6,3]=>162 [6,2,1]=>2062 [6,1,1,1]=>2934 [5,4]=>210 [5,3,1]=>3068 [5,2,2]=>1806 [5,2,1,1]=>14988 [5,1,1,1,1]=>8157 [4,4,1]=>1736 [4,3,2]=>4590 [4,3,1,1]=>18864 [4,2,2,1]=>20838 [4,2,1,1,1]=>43422 [4,1,1,1,1,1]=>9897 [3,3,3]=>855 [3,3,2,1]=>22680 [3,3,1,1,1]=>23349 [3,2,2,2]=>7930 [3,2,2,1,1]=>70206 [3,2,1,1,1,1]=>49569 [3,1,1,1,1,1,1]=>4414 [2,2,2,2,1]=>11056 [2,2,2,1,1,1]=>28768 [2,2,1,1,1,1,1]=>10194 [2,1,1,1,1,1,1,1]=>502 [1,1,1,1,1,1,1,1,1]=>1 [10]=>1 [9,1]=>46 [8,2]=>130 [8,1,1]=>787 [7,3]=>255 [7,2,1]=>3788 [7,1,1,1]=>6371 [6,4]=>372 [6,3,1]=>6426 [6,2,2]=>3868 [6,2,1,1]=>38224 [6,1,1,1,1]=>25761 [5,5]=>210 [5,4,1]=>8220 [5,3,2]=>11270 [5,3,1,1]=>55328 [5,2,2,1]=>63456 [5,2,1,1,1]=>165978 [5,1,1,1,1,1]=>50682 [4,4,2]=>6326 [4,4,1,1]=>31016 [4,3,3]=>7155 [4,3,2,1]=>156894 [4,3,1,1,1]=>203304 [4,2,2,2]=>28768 [4,2,2,1,1]=>325500 [4,2,1,1,1,1]=>316164 [4,1,1,1,1,1,1]=>44002 [3,3,3,1]=>28665 [3,3,2,2]=>46470 [3,3,2,1,1]=>346539 [3,3,1,1,1,1]=>166314 [3,2,2,2,1]=>232216 [3,2,2,1,1,1]=>635610 [3,2,1,1,1,1,1]=>245148 [3,1,1,1,1,1,1,1]=>13744 [2,2,2,2,2]=>11056 [2,2,2,2,1,1]=>141584 [2,2,2,1,1,1,1]=>166042 [2,2,1,1,1,1,1,1]=>34096 [2,1,1,1,1,1,1,1,1]=>1013 [1,1,1,1,1,1,1,1,1,1]=>1
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Description
Number of permutations whose sorted list of non zero multiplicities of the Lehmer code is the given partition.
References
[1] Hivert, F., Novelli, J.-C., Thibon, J.-Y. Multivariate generalizations of the Foata-Sch├╝tzenberger equidistribution MathSciNet:2509639 arXiv:math/0605060
Code
import collections
def part_of_perm(p):
    c = p.to_lehmer_code()
    return Partition(sorted([c.count(i) for i in range(len(p)) if i in c])[::-1])

@cached_function
def stat(N):
    res = collections.defaultdict(int)
    for p in Permutations(N):
        res[part_of_perm(p)] += 1
    return dict(res)

def statistic(L):
    return stat(L.size())[L]
Created
Sep 04, 2015 at 17:58 by Florent Hivert
Updated
Sep 15, 2015 at 15:49 by Christian Stump