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Statistic identifier: St001763

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Collection: Integer partitions

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Description: The Hurwitz number of an integer partition.

See [eq.(9),pg.21, 1].

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References: [1]   Hurwitz, A. Ueber Riemann'sche Flächen mit gegebenen Verzweigungspunkten [[MathSciNet:1510692]]

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Code:
def statistic(la):
    n = sum(la)
    c = len(la)
    return factorial(n + c - 2) * n^(c - 3) * prod(p^p / factorial(p - 1) for p in la)

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Statistic values:

[1]           => 1
[2]           => 1
[1,1]         => 1
[3]           => 3
[2,1]         => 8
[1,1,1]       => 24
[4]           => 16
[3,1]         => 81
[2,2]         => 96
[2,1,1]       => 480
[1,1,1,1]     => 2880
[5]           => 125
[4,1]         => 1024
[3,2]         => 1296
[3,1,1]       => 9720
[2,2,1]       => 11520
[2,1,1,1]     => 100800
[1,1,1,1,1]   => 1008000
[6]           => 1296
[5,1]         => 15625
[4,2]         => 20480
[4,1,1]       => 215040
[3,3]         => 21870
[3,2,1]       => 272160
[3,1,1,1]     => 3265920
[2,2,2]       => 322560
[2,2,1,1]     => 3870720
[2,1,1,1,1]   => 52254720
[1,1,1,1,1,1] => 783820800
[7]           => 16807
[6,1]         => 279936
[5,2]         => 375000
[5,1,1]       => 5250000
[4,3]         => 414720
[4,2,1]       => 6881280
[4,1,1,1]     => 108380160
[3,3,1]       => 7348320
[3,2,2]       => 8709120
[3,2,1,1]     => 137168640
[2,2,2,1]     => 162570240
[8]           => 262144
[7,1]         => 5764801
[6,2]         => 7838208
[6,1,1]       => 141087744
[5,3]         => 8859375
[5,2,1]       => 189000000
[4,4]         => 9175040
[4,3,1]       => 209018880
[4,2,2]       => 247726080
[3,3,2]       => 264539520
[9]           => 4782969
[8,1]         => 134217728
[7,2]         => 184473632
[6,3]         => 211631616
[5,4]         => 224000000
[10]          => 100000000

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Created: Jan 11, 2022 at 18:45 by Martin Rubey

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Last Updated: Dec 28, 2023 at 00:15 by Martin Rubey