Identifier
Values
([2],3) => [2] => 2
([1,1],3) => [1,1] => 2
([3,1],3) => [2,1] => 3
([2,1,1],3) => [1,1,1] => 3
([4,2],3) => [2,2] => 7
([3,1,1],3) => [2,1,1] => 5
([2,2,1,1],3) => [1,1,1,1] => 5
([5,3,1],3) => [2,2,1] => 10
([4,2,1,1],3) => [2,1,1,1] => 8
([3,2,2,1,1],3) => [1,1,1,1,1] => 8
([6,4,2],3) => [2,2,2] => 22
([5,3,1,1],3) => [2,2,1,1] => 17
([4,2,2,1,1],3) => [2,1,1,1,1] => 13
([3,3,2,2,1,1],3) => [1,1,1,1,1,1] => 13
([2],4) => [2] => 2
([1,1],4) => [1,1] => 2
([3],4) => [3] => 3
([2,1],4) => [2,1] => 3
([1,1,1],4) => [1,1,1] => 3
([4,1],4) => [3,1] => 5
([2,2],4) => [2,2] => 7
([3,1,1],4) => [2,1,1] => 5
([2,1,1,1],4) => [1,1,1,1] => 5
([5,2],4) => [3,2] => 10
([4,1,1],4) => [3,1,1] => 8
([3,2,1],4) => [2,2,1] => 10
([3,1,1,1],4) => [2,1,1,1] => 8
([2,2,1,1,1],4) => [1,1,1,1,1] => 8
([6,3],4) => [3,3] => 22
([5,2,1],4) => [3,2,1] => 14
([4,1,1,1],4) => [3,1,1,1] => 13
([4,2,2],4) => [2,2,2] => 22
([3,3,1,1],4) => [2,2,1,1] => 17
([3,2,1,1,1],4) => [2,1,1,1,1] => 13
([2,2,2,1,1,1],4) => [1,1,1,1,1,1] => 13
([2],5) => [2] => 2
([1,1],5) => [1,1] => 2
([3],5) => [3] => 3
([2,1],5) => [2,1] => 3
([1,1,1],5) => [1,1,1] => 3
([4],5) => [4] => 5
([3,1],5) => [3,1] => 5
([2,2],5) => [2,2] => 7
([2,1,1],5) => [2,1,1] => 5
([1,1,1,1],5) => [1,1,1,1] => 5
([5,1],5) => [4,1] => 8
([3,2],5) => [3,2] => 10
([4,1,1],5) => [3,1,1] => 8
([2,2,1],5) => [2,2,1] => 10
([3,1,1,1],5) => [2,1,1,1] => 8
([2,1,1,1,1],5) => [1,1,1,1,1] => 8
([6,2],5) => [4,2] => 17
([5,1,1],5) => [4,1,1] => 13
([3,3],5) => [3,3] => 22
([4,2,1],5) => [3,2,1] => 14
([4,1,1,1],5) => [3,1,1,1] => 13
([2,2,2],5) => [2,2,2] => 22
([3,2,1,1],5) => [2,2,1,1] => 17
([3,1,1,1,1],5) => [2,1,1,1,1] => 13
([2,2,1,1,1,1],5) => [1,1,1,1,1,1] => 13
([2],6) => [2] => 2
([1,1],6) => [1,1] => 2
([3],6) => [3] => 3
([2,1],6) => [2,1] => 3
([1,1,1],6) => [1,1,1] => 3
([4],6) => [4] => 5
([3,1],6) => [3,1] => 5
([2,2],6) => [2,2] => 7
([2,1,1],6) => [2,1,1] => 5
([1,1,1,1],6) => [1,1,1,1] => 5
([5],6) => [5] => 8
([4,1],6) => [4,1] => 8
([3,2],6) => [3,2] => 10
([3,1,1],6) => [3,1,1] => 8
([2,2,1],6) => [2,2,1] => 10
([2,1,1,1],6) => [2,1,1,1] => 8
([1,1,1,1,1],6) => [1,1,1,1,1] => 8
([6,1],6) => [5,1] => 13
([4,2],6) => [4,2] => 17
([5,1,1],6) => [4,1,1] => 13
([3,3],6) => [3,3] => 22
([3,2,1],6) => [3,2,1] => 14
([4,1,1,1],6) => [3,1,1,1] => 13
([2,2,2],6) => [2,2,2] => 22
([2,2,1,1],6) => [2,2,1,1] => 17
([3,1,1,1,1],6) => [2,1,1,1,1] => 13
([2,1,1,1,1,1],6) => [1,1,1,1,1,1] => 13
([7,2],6) => [5,2] => 27
([6,1,1],6) => [5,1,1] => 21
([4,3],6) => [4,3] => 32
([5,2,1],6) => [4,2,1] => 24
([5,1,1,1],6) => [4,1,1,1] => 21
([3,3,1],6) => [3,3,1] => 32
([3,2,2],6) => [3,2,2] => 32
([4,2,1,1],6) => [3,2,1,1] => 24
([4,1,1,1,1],6) => [3,1,1,1,1] => 21
([2,2,2,1],6) => [2,2,2,1] => 32
([3,2,1,1,1],6) => [2,2,1,1,1] => 27
([3,1,1,1,1,1],6) => [2,1,1,1,1,1] => 21
([2,2,1,1,1,1,1],6) => [1,1,1,1,1,1,1] => 21
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Description
The number of monomer-dimer tilings of a Ferrers diagram.
For a hook of length $n$, this is the $n$-th Fibonacci number.
Map
to bounded partition
Description
The (k-1)-bounded partition of a k-core.
Starting with a $k$-core, deleting all cells of hook length greater than or equal to $k$ yields a $(k-1)$-bounded partition [1, Theorem 7], see also [2, Section 1.2].