Identifier
Values
[3] => ([],3) => [1,1,1] => [1,1] => 1
[1,3] => ([(2,3)],4) => [2,1,1] => [1,1] => 1
[4] => ([],4) => [1,1,1,1] => [1,1,1] => 2
[1,1,3] => ([(2,3),(2,4),(3,4)],5) => [3,1,1] => [1,1] => 1
[1,4] => ([(3,4)],5) => [2,1,1,1] => [1,1,1] => 2
[2,3] => ([(2,4),(3,4)],5) => [3,1,1] => [1,1] => 1
[5] => ([],5) => [1,1,1,1,1] => [1,1,1,1] => 3
[1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => [1,1] => 1
[1,1,4] => ([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => [1,1,1] => 2
[1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => [1,1] => 1
[1,5] => ([(4,5)],6) => [2,1,1,1,1] => [1,1,1,1] => 3
[2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => [1,1] => 1
[2,4] => ([(3,5),(4,5)],6) => [3,1,1,1] => [1,1,1] => 2
[3,3] => ([(2,5),(3,5),(4,5)],6) => [4,1,1] => [1,1] => 1
[6] => ([],6) => [1,1,1,1,1,1] => [1,1,1,1,1] => 4
[1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
[1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
[1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
[1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => [1,1,1,1] => 3
[1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
[1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
[1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
[1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => [1,1,1,1,1] => 4
[2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
[2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
[2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
[2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => [1,1,1,1] => 3
[3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
[3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
[4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
[7] => ([],7) => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 5
[1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => [1,1,1,1] => 3
[1,1,3,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => [1,1] => 1
[1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => [1,1] => 1
[1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => [1,1] => 1
[1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => [1,1] => 1
[2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => [1,1] => 1
[2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => [1,1] => 1
[2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => [1,1] => 1
[3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => [1,1] => 1
[3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => [1,1] => 1
[4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => [1,1] => 1
[4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => [1,1,1] => 2
[8] => ([],8) => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 6
search for individual values
searching the database for the individual values of this statistic
Description
The Grundy value of Chomp on Ferrers diagrams.
Players take turns and choose a cell of the diagram, cutting off all cells below and to the right of this cell in English notation. The player who is left with the single cell partition looses. The traditional version is played on chocolate bars, see [1].
This statistic is the Grundy value of the partition, that is, the smallest non-negative integer which does not occur as value of a partition obtained by a single move.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
first row removal
Description
Removes the first entry of an integer partition