Identifier
Identifier
Values
[1] => 1
[1,1] => 2
[2] => 1
[1,1,1] => 3
[1,2] => 1
[2,1] => 1
[3] => 1
[1,1,1,1] => 4
[1,1,2] => 1
[1,2,1] => 1
[1,3] => 1
[2,1,1] => 1
[2,2] => 2
[3,1] => 1
[4] => 1
[1,1,1,1,1] => 5
[1,1,1,2] => 1
[1,1,2,1] => 1
[1,1,3] => 1
[1,2,1,1] => 1
[1,2,2] => 1
[1,3,1] => 1
[1,4] => 1
[2,1,1,1] => 1
[2,1,2] => 1
[2,2,1] => 1
[2,3] => 1
[3,1,1] => 1
[3,2] => 1
[4,1] => 1
[5] => 1
[1,1,1,1,1,1] => 6
[1,1,1,1,2] => 1
[1,1,1,2,1] => 1
[1,1,1,3] => 1
[1,1,2,1,1] => 1
[1,1,2,2] => 2
[1,1,3,1] => 1
[1,1,4] => 1
[1,2,1,1,1] => 1
[1,2,1,2] => 2
[1,2,2,1] => 2
[1,2,3] => 1
[1,3,1,1] => 1
[1,3,2] => 1
[1,4,1] => 1
[1,5] => 1
[2,1,1,1,1] => 1
[2,1,1,2] => 2
[2,1,2,1] => 2
[2,1,3] => 1
[2,2,1,1] => 2
[2,2,2] => 3
[2,3,1] => 1
[2,4] => 1
[3,1,1,1] => 1
[3,1,2] => 1
[3,2,1] => 1
[3,3] => 2
[4,1,1] => 1
[4,2] => 1
[5,1] => 1
[6] => 1
[1,1,1,1,1,1,1] => 7
[1,1,1,1,1,2] => 1
[1,1,1,1,2,1] => 1
[1,1,1,1,3] => 1
[1,1,1,2,1,1] => 1
[1,1,1,2,2] => 2
[1,1,1,3,1] => 1
[1,1,1,4] => 1
[1,1,2,1,1,1] => 1
[1,1,2,1,2] => 2
[1,1,2,2,1] => 2
[1,1,2,3] => 1
[1,1,3,1,1] => 1
[1,1,3,2] => 1
[1,1,4,1] => 1
[1,1,5] => 1
[1,2,1,1,1,1] => 1
[1,2,1,1,2] => 2
[1,2,1,2,1] => 2
[1,2,1,3] => 1
[1,2,2,1,1] => 2
[1,2,2,2] => 1
[1,2,3,1] => 1
[1,2,4] => 1
[1,3,1,1,1] => 1
[1,3,1,2] => 1
[1,3,2,1] => 1
[1,3,3] => 1
[1,4,1,1] => 1
[1,4,2] => 1
[1,5,1] => 1
[1,6] => 1
[2,1,1,1,1,1] => 1
[2,1,1,1,2] => 2
[2,1,1,2,1] => 2
[2,1,1,3] => 1
[2,1,2,1,1] => 2
[2,1,2,2] => 1
[2,1,3,1] => 1
[2,1,4] => 1
[2,2,1,1,1] => 2
[2,2,1,2] => 1
[2,2,2,1] => 1
[2,2,3] => 1
[2,3,1,1] => 1
[2,3,2] => 1
[2,4,1] => 1
[2,5] => 1
[3,1,1,1,1] => 1
[3,1,1,2] => 1
[3,1,2,1] => 1
[3,1,3] => 1
[3,2,1,1] => 1
[3,2,2] => 1
[3,3,1] => 1
[3,4] => 1
[4,1,1,1] => 1
[4,1,2] => 1
[4,2,1] => 1
[4,3] => 1
[5,1,1] => 1
[5,2] => 1
[6,1] => 1
[7] => 1
[1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,2] => 1
[1,1,1,1,1,2,1] => 1
[1,1,1,1,1,3] => 1
[1,1,1,1,2,1,1] => 1
[1,1,1,1,2,2] => 2
[1,1,1,1,3,1] => 1
[1,1,1,1,4] => 1
[1,1,1,2,1,1,1] => 1
[1,1,1,2,1,2] => 2
[1,1,1,2,2,1] => 2
[1,1,1,2,3] => 1
[1,1,1,3,1,1] => 1
[1,1,1,3,2] => 1
[1,1,1,4,1] => 1
[1,1,1,5] => 1
[1,1,2,1,1,1,1] => 1
[1,1,2,1,1,2] => 2
[1,1,2,1,2,1] => 2
[1,1,2,1,3] => 1
[1,1,2,2,1,1] => 2
[1,1,2,2,2] => 2
[1,1,2,3,1] => 1
[1,1,2,4] => 1
[1,1,3,1,1,1] => 1
[1,1,3,1,2] => 1
[1,1,3,2,1] => 1
[1,1,3,3] => 2
[1,1,4,1,1] => 1
[1,1,4,2] => 1
[1,1,5,1] => 1
[1,1,6] => 1
[1,2,1,1,1,1,1] => 1
[1,2,1,1,1,2] => 2
[1,2,1,1,2,1] => 2
[1,2,1,1,3] => 1
[1,2,1,2,1,1] => 2
[1,2,1,2,2] => 2
[1,2,1,3,1] => 1
[1,2,1,4] => 1
[1,2,2,1,1,1] => 2
[1,2,2,1,2] => 2
[1,2,2,2,1] => 2
[1,2,2,3] => 1
[1,2,3,1,1] => 1
[1,2,3,2] => 1
[1,2,4,1] => 1
[1,2,5] => 1
[1,3,1,1,1,1] => 1
[1,3,1,1,2] => 1
[1,3,1,2,1] => 1
[1,3,1,3] => 2
[1,3,2,1,1] => 1
[1,3,2,2] => 1
[1,3,3,1] => 2
[1,3,4] => 1
[1,4,1,1,1] => 1
[1,4,1,2] => 1
[1,4,2,1] => 1
[1,4,3] => 1
[1,5,1,1] => 1
[1,5,2] => 1
[1,6,1] => 1
[1,7] => 1
[2,1,1,1,1,1,1] => 1
[2,1,1,1,1,2] => 2
[2,1,1,1,2,1] => 2
[2,1,1,1,3] => 1
[2,1,1,2,1,1] => 2
[2,1,1,2,2] => 2
[2,1,1,3,1] => 1
[2,1,1,4] => 1
[2,1,2,1,1,1] => 2
[2,1,2,1,2] => 2
[2,1,2,2,1] => 2
[2,1,2,3] => 1
[2,1,3,1,1] => 1
[2,1,3,2] => 1
[2,1,4,1] => 1
[2,1,5] => 1
[2,2,1,1,1,1] => 2
[2,2,1,1,2] => 2
[2,2,1,2,1] => 2
[2,2,1,3] => 1
[2,2,2,1,1] => 2
[2,2,2,2] => 4
[2,2,3,1] => 1
[2,2,4] => 1
[2,3,1,1,1] => 1
[2,3,1,2] => 1
[2,3,2,1] => 1
[2,3,3] => 1
[2,4,1,1] => 1
[2,4,2] => 1
[2,5,1] => 1
[2,6] => 1
[3,1,1,1,1,1] => 1
[3,1,1,1,2] => 1
[3,1,1,2,1] => 1
[3,1,1,3] => 2
[3,1,2,1,1] => 1
[3,1,2,2] => 1
[3,1,3,1] => 2
[3,1,4] => 1
[3,2,1,1,1] => 1
[3,2,1,2] => 1
[3,2,2,1] => 1
[3,2,3] => 1
[3,3,1,1] => 2
[3,3,2] => 1
[3,4,1] => 1
[3,5] => 1
[4,1,1,1,1] => 1
[4,1,1,2] => 1
[4,1,2,1] => 1
[4,1,3] => 1
[4,2,1,1] => 1
[4,2,2] => 1
[4,3,1] => 1
[4,4] => 2
[5,1,1,1] => 1
[5,1,2] => 1
[5,2,1] => 1
[5,3] => 1
[6,1,1] => 1
[6,2] => 1
[7,1] => 1
[8] => 1
[1,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,2] => 1
[1,1,1,1,1,1,2,1] => 1
[1,1,1,1,1,1,3] => 1
[1,1,1,1,1,2,1,1] => 1
[1,1,1,1,1,2,2] => 2
[1,1,1,1,1,3,1] => 1
[1,1,1,1,1,4] => 1
[1,1,1,1,2,1,1,1] => 1
[1,1,1,1,2,1,2] => 2
[1,1,1,1,2,2,1] => 2
[1,1,1,1,2,3] => 1
[1,1,1,1,3,1,1] => 1
[1,1,1,1,3,2] => 1
[1,1,1,1,4,1] => 1
[1,1,1,1,5] => 1
[1,1,1,2,1,1,1,1] => 1
[1,1,1,2,1,1,2] => 2
[1,1,1,2,1,2,1] => 2
[1,1,1,2,1,3] => 1
[1,1,1,2,2,1,1] => 2
[1,1,1,2,2,2] => 3
[1,1,1,2,3,1] => 1
[1,1,1,2,4] => 1
[1,1,1,3,1,1,1] => 1
[1,1,1,3,1,2] => 1
[1,1,1,3,2,1] => 1
[1,1,1,3,3] => 2
[1,1,1,4,1,1] => 1
[1,1,1,4,2] => 1
[1,1,1,5,1] => 1
[1,1,1,6] => 1
[1,1,2,1,1,1,1,1] => 1
[1,1,2,1,1,1,2] => 2
[1,1,2,1,1,2,1] => 2
[1,1,2,1,1,3] => 1
[1,1,2,1,2,1,1] => 2
[1,1,2,1,2,2] => 3
[1,1,2,1,3,1] => 1
[1,1,2,1,4] => 1
[1,1,2,2,1,1,1] => 2
[1,1,2,2,1,2] => 3
[1,1,2,2,2,1] => 3
[1,1,2,2,3] => 1
[1,1,2,3,1,1] => 1
[1,1,2,3,2] => 1
[1,1,2,4,1] => 1
[1,1,2,5] => 1
[1,1,3,1,1,1,1] => 1
[1,1,3,1,1,2] => 1
[1,1,3,1,2,1] => 1
[1,1,3,1,3] => 2
[1,1,3,2,1,1] => 1
[1,1,3,2,2] => 1
[1,1,3,3,1] => 2
[1,1,3,4] => 1
[1,1,4,1,1,1] => 1
[1,1,4,1,2] => 1
[1,1,4,2,1] => 1
[1,1,4,3] => 1
[1,1,5,1,1] => 1
[1,1,5,2] => 1
[1,1,6,1] => 1
[1,1,7] => 1
[1,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,2] => 2
[1,2,1,1,1,2,1] => 2
[1,2,1,1,1,3] => 1
[1,2,1,1,2,1,1] => 2
[1,2,1,1,2,2] => 3
[1,2,1,1,3,1] => 1
[1,2,1,1,4] => 1
[1,2,1,2,1,1,1] => 2
[1,2,1,2,1,2] => 3
[1,2,1,2,2,1] => 3
[1,2,1,2,3] => 1
[1,2,1,3,1,1] => 1
[1,2,1,3,2] => 1
[1,2,1,4,1] => 1
[1,2,1,5] => 1
[1,2,2,1,1,1,1] => 2
[1,2,2,1,1,2] => 3
[1,2,2,1,2,1] => 3
[1,2,2,1,3] => 1
[1,2,2,2,1,1] => 3
[1,2,2,2,2] => 1
[1,2,2,3,1] => 1
[1,2,2,4] => 1
[1,2,3,1,1,1] => 1
[1,2,3,1,2] => 1
[1,2,3,2,1] => 1
[1,2,3,3] => 1
[1,2,4,1,1] => 1
[1,2,4,2] => 1
[1,2,5,1] => 1
[1,2,6] => 1
[1,3,1,1,1,1,1] => 1
[1,3,1,1,1,2] => 1
[1,3,1,1,2,1] => 1
[1,3,1,1,3] => 2
[1,3,1,2,1,1] => 1
[1,3,1,2,2] => 1
[1,3,1,3,1] => 2
[1,3,1,4] => 1
[1,3,2,1,1,1] => 1
[1,3,2,1,2] => 1
[1,3,2,2,1] => 1
[1,3,2,3] => 1
[1,3,3,1,1] => 2
[1,3,3,2] => 1
[1,3,4,1] => 1
[1,3,5] => 1
[1,4,1,1,1,1] => 1
[1,4,1,1,2] => 1
[1,4,1,2,1] => 1
[1,4,1,3] => 1
[1,4,2,1,1] => 1
[1,4,2,2] => 1
[1,4,3,1] => 1
[1,4,4] => 1
[1,5,1,1,1] => 1
[1,5,1,2] => 1
[1,5,2,1] => 1
[1,5,3] => 1
[1,6,1,1] => 1
[1,6,2] => 1
[1,7,1] => 1
[1,8] => 1
[2,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2] => 2
[2,1,1,1,1,2,1] => 2
[2,1,1,1,1,3] => 1
[2,1,1,1,2,1,1] => 2
[2,1,1,1,2,2] => 3
[2,1,1,1,3,1] => 1
[2,1,1,1,4] => 1
[2,1,1,2,1,1,1] => 2
[2,1,1,2,1,2] => 3
[2,1,1,2,2,1] => 3
[2,1,1,2,3] => 1
[2,1,1,3,1,1] => 1
[2,1,1,3,2] => 1
[2,1,1,4,1] => 1
[2,1,1,5] => 1
[2,1,2,1,1,1,1] => 2
[2,1,2,1,1,2] => 3
[2,1,2,1,2,1] => 3
[2,1,2,1,3] => 1
[2,1,2,2,1,1] => 3
[2,1,2,2,2] => 1
[2,1,2,3,1] => 1
[2,1,2,4] => 1
[2,1,3,1,1,1] => 1
[2,1,3,1,2] => 1
[2,1,3,2,1] => 1
[2,1,3,3] => 1
[2,1,4,1,1] => 1
[2,1,4,2] => 1
[2,1,5,1] => 1
[2,1,6] => 1
[2,2,1,1,1,1,1] => 2
[2,2,1,1,1,2] => 3
[2,2,1,1,2,1] => 3
[2,2,1,1,3] => 1
[2,2,1,2,1,1] => 3
[2,2,1,2,2] => 1
[2,2,1,3,1] => 1
[2,2,1,4] => 1
[2,2,2,1,1,1] => 3
[2,2,2,1,2] => 1
[2,2,2,2,1] => 1
[2,2,2,3] => 1
[2,2,3,1,1] => 1
[2,2,3,2] => 1
[2,2,4,1] => 1
[2,2,5] => 1
[2,3,1,1,1,1] => 1
[2,3,1,1,2] => 1
[2,3,1,2,1] => 1
[2,3,1,3] => 1
[2,3,2,1,1] => 1
[2,3,2,2] => 1
[2,3,3,1] => 1
[2,3,4] => 1
[2,4,1,1,1] => 1
[2,4,1,2] => 1
[2,4,2,1] => 1
[2,4,3] => 1
[2,5,1,1] => 1
[2,5,2] => 1
[2,6,1] => 1
[2,7] => 1
[3,1,1,1,1,1,1] => 1
[3,1,1,1,1,2] => 1
[3,1,1,1,2,1] => 1
[3,1,1,1,3] => 2
[3,1,1,2,1,1] => 1
[3,1,1,2,2] => 1
[3,1,1,3,1] => 2
[3,1,1,4] => 1
[3,1,2,1,1,1] => 1
[3,1,2,1,2] => 1
[3,1,2,2,1] => 1
[3,1,2,3] => 1
[3,1,3,1,1] => 2
[3,1,3,2] => 1
[3,1,4,1] => 1
[3,1,5] => 1
[3,2,1,1,1,1] => 1
[3,2,1,1,2] => 1
[3,2,1,2,1] => 1
[3,2,1,3] => 1
[3,2,2,1,1] => 1
[3,2,2,2] => 1
[3,2,3,1] => 1
[3,2,4] => 1
[3,3,1,1,1] => 2
[3,3,1,2] => 1
[3,3,2,1] => 1
[3,3,3] => 3
[3,4,1,1] => 1
[3,4,2] => 1
[3,5,1] => 1
[3,6] => 1
[4,1,1,1,1,1] => 1
[4,1,1,1,2] => 1
[4,1,1,2,1] => 1
[4,1,1,3] => 1
[4,1,2,1,1] => 1
[4,1,2,2] => 1
[4,1,3,1] => 1
[4,1,4] => 1
[4,2,1,1,1] => 1
[4,2,1,2] => 1
[4,2,2,1] => 1
[4,2,3] => 1
[4,3,1,1] => 1
[4,3,2] => 1
[4,4,1] => 1
[4,5] => 1
[5,1,1,1,1] => 1
[5,1,1,2] => 1
[5,1,2,1] => 1
[5,1,3] => 1
[5,2,1,1] => 1
[5,2,2] => 1
[5,3,1] => 1
[5,4] => 1
[6,1,1,1] => 1
[6,1,2] => 1
[6,2,1] => 1
[6,3] => 1
[7,1,1] => 1
[7,2] => 1
[8,1] => 1
[9] => 1
click to show generating function       
Description
The minimal number of repetitions of an integer composition.
Code
def statistic(C):
    C = list(C)
    seq = [ C.count(i) for i in [ 1 .. max(C) ] if C.count(i) ]
    return min(seq)
Created
Jul 16, 2017 at 08:16 by Christian Stump
Updated
Nov 19, 2017 at 22:01 by Christian Stump