- FindStat

Identifier

St001763: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        [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