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Identifier

St001933: Integer partitions ⟶ ℤ

Values

[1] => 1

[2] => 1

[1,1] => 2

[3] => 1

[2,1] => 1

[1,1,1] => 3

[4] => 1

[3,1] => 1

[2,2] => 2

[2,1,1] => 2

[1,1,1,1] => 4

[5] => 1

[4,1] => 1

[3,2] => 1

[3,1,1] => 2

[2,2,1] => 2

[2,1,1,1] => 3

[1,1,1,1,1] => 5

[6] => 1

[5,1] => 1

[4,2] => 1

[4,1,1] => 2

[3,3] => 2

[3,2,1] => 1

[3,1,1,1] => 3

[2,2,2] => 3

[2,2,1,1] => 2

[2,1,1,1,1] => 4

[1,1,1,1,1,1] => 6

[7] => 1

[6,1] => 1

[5,2] => 1

[5,1,1] => 2

[4,3] => 1

[4,2,1] => 1

[4,1,1,1] => 3

[3,3,1] => 2

[3,2,2] => 2

[3,2,1,1] => 2

[3,1,1,1,1] => 4

[2,2,2,1] => 3

[2,2,1,1,1] => 3

[2,1,1,1,1,1] => 5

[1,1,1,1,1,1,1] => 7

[8] => 1

[7,1] => 1

[6,2] => 1

[6,1,1] => 2

[5,3] => 1

[5,2,1] => 1

[5,1,1,1] => 3

[4,4] => 2

[4,3,1] => 1

[4,2,2] => 2

[4,2,1,1] => 2

[4,1,1,1,1] => 4

[3,3,2] => 2

[3,3,1,1] => 2

[3,2,2,1] => 2

[3,2,1,1,1] => 3

[3,1,1,1,1,1] => 5

[2,2,2,2] => 4

[2,2,2,1,1] => 3

[2,2,1,1,1,1] => 4

[2,1,1,1,1,1,1] => 6

[1,1,1,1,1,1,1,1] => 8

[9] => 1

[8,1] => 1

[7,2] => 1

[7,1,1] => 2

[6,3] => 1

[6,2,1] => 1

[6,1,1,1] => 3

[5,4] => 1

[5,3,1] => 1

[5,2,2] => 2

[5,2,1,1] => 2

[5,1,1,1,1] => 4

[4,4,1] => 2

[4,3,2] => 1

[4,3,1,1] => 2

[4,2,2,1] => 2

[4,2,1,1,1] => 3

[4,1,1,1,1,1] => 5

[3,3,3] => 3

[3,3,2,1] => 2

[3,3,1,1,1] => 3

[3,2,2,2] => 3

[3,2,2,1,1] => 2

[3,2,1,1,1,1] => 4

[3,1,1,1,1,1,1] => 6

[2,2,2,2,1] => 4

[2,2,2,1,1,1] => 3

[2,2,1,1,1,1,1] => 5

[2,1,1,1,1,1,1,1] => 7

[1,1,1,1,1,1,1,1,1] => 9

[10] => 1

[9,1] => 1

[8,2] => 1

[8,1,1] => 2

[7,3] => 1

>>> Load all 1200 entries. <<<

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$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = 2\ q + q^{3}$

$F_{4} = 2\ q + 2\ q^{2} + q^{4}$

$F_{5} = 3\ q + 2\ q^{2} + q^{3} + q^{5}$

$F_{6} = 4\ q + 3\ q^{2} + 2\ q^{3} + q^{4} + q^{6}$

$F_{7} = 5\ q + 4\ q^{2} + 3\ q^{3} + q^{4} + q^{5} + q^{7}$

$F_{8} = 6\ q + 7\ q^{2} + 3\ q^{3} + 3\ q^{4} + q^{5} + q^{6} + q^{8}$

$F_{9} = 8\ q + 8\ q^{2} + 6\ q^{3} + 3\ q^{4} + 2\ q^{5} + q^{6} + q^{7} + q^{9}$

$F_{10} = 10\ q + 12\ q^{2} + 7\ q^{3} + 5\ q^{4} + 3\ q^{5} + 2\ q^{6} + q^{7} + q^{8} + q^{10}$

$F_{11} = 12\ q + 15\ q^{2} + 11\ q^{3} + 6\ q^{4} + 5\ q^{5} + 2\ q^{6} + 2\ q^{7} + q^{8} + q^{9} + q^{11}$

$F_{12} = 15\ q + 21\ q^{2} + 14\ q^{3} + 10\ q^{4} + 5\ q^{5} + 5\ q^{6} + 2\ q^{7} + 2\ q^{8} + q^{9} + q^{10} + q^{12}$

$F_{13} = 18\ q + 26\ q^{2} + 20\ q^{3} + 12\ q^{4} + 9\ q^{5} + 5\ q^{6} + 4\ q^{7} + 2\ q^{8} + 2\ q^{9} + q^{10} + q^{11} + q^{13}$

$F_{14} = 22\ q + 35\ q^{2} + 25\ q^{3} + 18\ q^{4} + 11\ q^{5} + 8\ q^{6} + 5\ q^{7} + 4\ q^{8} + 2\ q^{9} + 2\ q^{10} + q^{11} + q^{12} + q^{14}$

$F_{15} = 27\ q + 43\ q^{2} + 35\ q^{3} + 22\ q^{4} + 16\ q^{5} + 10\ q^{6} + 8\ q^{7} + 4\ q^{8} + 4\ q^{9} + 2\ q^{10} + 2\ q^{11} + q^{12} + q^{13} + q^{15}$

$F_{16} = 32\ q + 57\ q^{2} + 43\ q^{3} + 32\ q^{4} + 20\ q^{5} + 15\ q^{6} + 9\ q^{7} + 8\ q^{8} + 4\ q^{9} + 4\ q^{10} + 2\ q^{11} + 2\ q^{12} + q^{13} + q^{14} + q^{16}$

Description

The largest multiplicity of a part in an integer partition.

Code

def statistic(pi):
    return max(pi.to_exp(), default=0)

Created

Nov 24, 2023 at 15:29 by Martin Rubey

Updated

Nov 24, 2023 at 15:29 by Martin Rubey