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Identifier
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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Description
The Hurwitz number of an integer partition.
See [eq.(9),pg.21, 1].
References
[1] Hurwitz, A. Ueber Riemann'sche Flächen mit gegebenen Verzweigungspunkten MathSciNet:1510692
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)
Created
Jan 11, 2022 at 18:45 by Martin Rubey
Updated
Dec 28, 2023 at 00:15 by Martin Rubey