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Statistic identifier: St001128
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Collection: Integer partitions
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Description: The exponens consonantiae of a partition.
This is the quotient of the least common multiple and the greatest common divior of the parts of the partiton. See [1, Caput sextum, §19-§22].
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References: [1] Euler, Leonhard. Tentamen novae theoriae musicae ex certissimis harmoniae principiis dilucide expositae. ex typographia Academiae scientiarum, 1739.
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Code:
def statistic(p):
return lcm(p)/gcd(p)
-----------------------------------------------------------------------------
Statistic values:
[2] => 1
[1,1] => 1
[3] => 1
[2,1] => 2
[1,1,1] => 1
[4] => 1
[3,1] => 3
[2,2] => 1
[2,1,1] => 2
[1,1,1,1] => 1
[5] => 1
[4,1] => 4
[3,2] => 6
[3,1,1] => 3
[2,2,1] => 2
[2,1,1,1] => 2
[1,1,1,1,1] => 1
[6] => 1
[5,1] => 5
[4,2] => 2
[4,1,1] => 4
[3,3] => 1
[3,2,1] => 6
[3,1,1,1] => 3
[2,2,2] => 1
[2,2,1,1] => 2
[2,1,1,1,1] => 2
[1,1,1,1,1,1] => 1
[7] => 1
[6,1] => 6
[5,2] => 10
[5,1,1] => 5
[4,3] => 12
[4,2,1] => 4
[4,1,1,1] => 4
[3,3,1] => 3
[3,2,2] => 6
[3,2,1,1] => 6
[3,1,1,1,1] => 3
[2,2,2,1] => 2
[2,2,1,1,1] => 2
[2,1,1,1,1,1] => 2
[1,1,1,1,1,1,1] => 1
[8] => 1
[7,1] => 7
[6,2] => 3
[6,1,1] => 6
[5,3] => 15
[5,2,1] => 10
[5,1,1,1] => 5
[4,4] => 1
[4,3,1] => 12
[4,2,2] => 2
[4,2,1,1] => 4
[4,1,1,1,1] => 4
[3,3,2] => 6
[3,3,1,1] => 3
[3,2,2,1] => 6
[3,2,1,1,1] => 6
[3,1,1,1,1,1] => 3
[2,2,2,2] => 1
[2,2,2,1,1] => 2
[2,2,1,1,1,1] => 2
[2,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1] => 1
[9] => 1
[8,1] => 8
[7,2] => 14
[7,1,1] => 7
[6,3] => 2
[6,2,1] => 6
[6,1,1,1] => 6
[5,4] => 20
[5,3,1] => 15
[5,2,2] => 10
[5,2,1,1] => 10
[5,1,1,1,1] => 5
[4,4,1] => 4
[4,3,2] => 12
[4,3,1,1] => 12
[4,2,2,1] => 4
[4,2,1,1,1] => 4
[4,1,1,1,1,1] => 4
[3,3,3] => 1
[3,3,2,1] => 6
[3,3,1,1,1] => 3
[3,2,2,2] => 6
[3,2,2,1,1] => 6
[3,2,1,1,1,1] => 6
[3,1,1,1,1,1,1] => 3
[2,2,2,2,1] => 2
[2,2,2,1,1,1] => 2
[2,2,1,1,1,1,1] => 2
[2,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1] => 1
[10] => 1
[9,1] => 9
[8,2] => 4
[8,1,1] => 8
[7,3] => 21
[7,2,1] => 14
[7,1,1,1] => 7
[6,4] => 6
[6,3,1] => 6
[6,2,2] => 3
[6,2,1,1] => 6
[6,1,1,1,1] => 6
[5,5] => 1
[5,4,1] => 20
[5,3,2] => 30
[5,3,1,1] => 15
[5,2,2,1] => 10
[5,2,1,1,1] => 10
[5,1,1,1,1,1] => 5
[4,4,2] => 2
[4,4,1,1] => 4
[4,3,3] => 12
[4,3,2,1] => 12
[4,3,1,1,1] => 12
[4,2,2,2] => 2
[4,2,2,1,1] => 4
[4,2,1,1,1,1] => 4
[4,1,1,1,1,1,1] => 4
[3,3,3,1] => 3
[3,3,2,2] => 6
[3,3,2,1,1] => 6
[3,3,1,1,1,1] => 3
[3,2,2,2,1] => 6
[3,2,2,1,1,1] => 6
[3,2,1,1,1,1,1] => 6
[3,1,1,1,1,1,1,1] => 3
[2,2,2,2,2] => 1
[2,2,2,2,1,1] => 2
[2,2,2,1,1,1,1] => 2
[2,2,1,1,1,1,1,1] => 2
[2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1] => 1
[11] => 1
[10,1] => 10
[9,2] => 18
[9,1,1] => 9
[8,3] => 24
[8,2,1] => 8
[8,1,1,1] => 8
[7,4] => 28
[7,3,1] => 21
[7,2,2] => 14
[7,2,1,1] => 14
[7,1,1,1,1] => 7
[6,5] => 30
[6,4,1] => 12
[6,3,2] => 6
[6,3,1,1] => 6
[6,2,2,1] => 6
[6,2,1,1,1] => 6
[6,1,1,1,1,1] => 6
[5,5,1] => 5
[5,4,2] => 20
[5,4,1,1] => 20
[5,3,3] => 15
[5,3,2,1] => 30
[5,3,1,1,1] => 15
[5,2,2,2] => 10
[5,2,2,1,1] => 10
[5,2,1,1,1,1] => 10
[5,1,1,1,1,1,1] => 5
[4,4,3] => 12
[4,4,2,1] => 4
[4,4,1,1,1] => 4
[4,3,3,1] => 12
[4,3,2,2] => 12
[4,3,2,1,1] => 12
[4,3,1,1,1,1] => 12
[4,2,2,2,1] => 4
[4,2,2,1,1,1] => 4
[4,2,1,1,1,1,1] => 4
[4,1,1,1,1,1,1,1] => 4
[3,3,3,2] => 6
[3,3,3,1,1] => 3
[3,3,2,2,1] => 6
[3,3,2,1,1,1] => 6
[3,3,1,1,1,1,1] => 3
[3,2,2,2,2] => 6
[3,2,2,2,1,1] => 6
[3,2,2,1,1,1,1] => 6
[3,2,1,1,1,1,1,1] => 6
[3,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,1] => 2
[2,2,2,2,1,1,1] => 2
[2,2,2,1,1,1,1,1] => 2
[2,2,1,1,1,1,1,1,1] => 2
[2,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1] => 1
[12] => 1
[11,1] => 11
[10,2] => 5
[10,1,1] => 10
[9,3] => 3
[9,2,1] => 18
[9,1,1,1] => 9
[8,4] => 2
[8,3,1] => 24
[8,2,2] => 4
[8,2,1,1] => 8
[8,1,1,1,1] => 8
[7,5] => 35
[7,4,1] => 28
[7,3,2] => 42
[7,3,1,1] => 21
[7,2,2,1] => 14
[7,2,1,1,1] => 14
[7,1,1,1,1,1] => 7
[6,6] => 1
[6,5,1] => 30
[6,4,2] => 6
[6,4,1,1] => 12
[6,3,3] => 2
[6,3,2,1] => 6
[6,3,1,1,1] => 6
[6,2,2,2] => 3
[6,2,2,1,1] => 6
[6,2,1,1,1,1] => 6
[6,1,1,1,1,1,1] => 6
[5,5,2] => 10
[5,5,1,1] => 5
[5,4,3] => 60
[5,4,2,1] => 20
[5,4,1,1,1] => 20
[5,3,3,1] => 15
[5,3,2,2] => 30
[5,3,2,1,1] => 30
[5,3,1,1,1,1] => 15
[5,2,2,2,1] => 10
[5,2,2,1,1,1] => 10
[5,2,1,1,1,1,1] => 10
[5,1,1,1,1,1,1,1] => 5
[4,4,4] => 1
[4,4,3,1] => 12
[4,4,2,2] => 2
[4,4,2,1,1] => 4
[4,4,1,1,1,1] => 4
[4,3,3,2] => 12
[4,3,3,1,1] => 12
[4,3,2,2,1] => 12
[4,3,2,1,1,1] => 12
[4,3,1,1,1,1,1] => 12
[4,2,2,2,2] => 2
[4,2,2,2,1,1] => 4
[4,2,2,1,1,1,1] => 4
[4,2,1,1,1,1,1,1] => 4
[4,1,1,1,1,1,1,1,1] => 4
[3,3,3,3] => 1
[3,3,3,2,1] => 6
[3,3,3,1,1,1] => 3
[3,3,2,2,2] => 6
[3,3,2,2,1,1] => 6
[3,3,2,1,1,1,1] => 6
[3,3,1,1,1,1,1,1] => 3
[3,2,2,2,2,1] => 6
[3,2,2,2,1,1,1] => 6
[3,2,2,1,1,1,1,1] => 6
[3,2,1,1,1,1,1,1,1] => 6
[3,1,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,2] => 1
[2,2,2,2,2,1,1] => 2
[2,2,2,2,1,1,1,1] => 2
[2,2,2,1,1,1,1,1,1] => 2
[2,2,1,1,1,1,1,1,1,1] => 2
[2,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1] => 1
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Created: Mar 21, 2018 at 13:36 by Martin Rubey
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Last Updated: Mar 21, 2018 at 13:36 by Martin Rubey