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Statistic identifier: St000275
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Collection: Integer partitions
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Description: Number of permutations whose sorted list of non zero multiplicities of the Lehmer code is the given partition.
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References: [1] Hivert, F., Novelli, J.-C., Thibon, J.-Y. Multivariate generalizations of the Foata-Schützenberger equidistribution [[MathSciNet:2509639]] [[arXiv:math/0605060]]
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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]
-----------------------------------------------------------------------------
Statistic values:
[] => 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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Created: Sep 04, 2015 at 17:58 by Florent Hivert
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Last Updated: Sep 15, 2015 at 15:49 by Christian Stump