- FindStat

Identifier

Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000147: Integer partitions ⟶ ℤ

Values

[1] => [] => 0

[2] => [] => 0

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

[3] => [] => 0

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

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

[4] => [] => 0

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

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

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

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

[5] => [] => 0

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

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

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

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

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

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

[6] => [] => 0

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

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

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

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

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

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

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

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

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

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

[7] => [] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[8] => [] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[9] => [] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[10] => [] => 0

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

[8,2] => [2] => 2

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

[7,3] => [3] => 3

>>> Load all 1396 entries. <<<

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$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 1 + 2\ q$

$F_{4} = 1 + 3\ q + q^{2}$

$F_{5} = 1 + 4\ q + 2\ q^{2}$

$F_{6} = 1 + 5\ q + 4\ q^{2} + q^{3}$

$F_{7} = 1 + 6\ q + 6\ q^{2} + 2\ q^{3}$

$F_{8} = 1 + 7\ q + 9\ q^{2} + 4\ q^{3} + q^{4}$

$F_{9} = 1 + 8\ q + 12\ q^{2} + 7\ q^{3} + 2\ q^{4}$

$F_{10} = 1 + 9\ q + 16\ q^{2} + 11\ q^{3} + 4\ q^{4} + q^{5}$

$F_{11} = 1 + 10\ q + 20\ q^{2} + 16\ q^{3} + 7\ q^{4} + 2\ q^{5}$

$F_{12} = 1 + 11\ q + 25\ q^{2} + 23\ q^{3} + 12\ q^{4} + 4\ q^{5} + q^{6}$

$F_{13} = 1 + 12\ q + 30\ q^{2} + 31\ q^{3} + 18\ q^{4} + 7\ q^{5} + 2\ q^{6}$

$F_{14} = 1 + 13\ q + 36\ q^{2} + 41\ q^{3} + 27\ q^{4} + 12\ q^{5} + 4\ q^{6} + q^{7}$

$F_{15} = 1 + 14\ q + 42\ q^{2} + 53\ q^{3} + 38\ q^{4} + 19\ q^{5} + 7\ q^{6} + 2\ q^{7}$

$F_{16} = 1 + 15\ q + 49\ q^{2} + 67\ q^{3} + 53\ q^{4} + 29\ q^{5} + 12\ q^{6} + 4\ q^{7} + q^{8}$

$F_{17} = 1 + 16\ q + 56\ q^{2} + 83\ q^{3} + 71\ q^{4} + 42\ q^{5} + 19\ q^{6} + 7\ q^{7} + 2\ q^{8}$

Description

The largest part of an integer partition.

Map

first row removal

Description

Removes the first entry of an integer partition