Processing math: 100%

Identifier
Values
0 => [1] => [1] => 1
1 => [1] => [1] => 1
00 => [2] => [1,1] => 2
01 => [1,1] => [2] => 1
10 => [1,1] => [2] => 1
11 => [2] => [1,1] => 2
000 => [3] => [1,1,1] => 3
001 => [2,1] => [2,1] => 2
010 => [1,1,1] => [3] => 1
011 => [1,2] => [1,2] => 2
100 => [1,2] => [1,2] => 2
101 => [1,1,1] => [3] => 1
110 => [2,1] => [2,1] => 2
111 => [3] => [1,1,1] => 3
0000 => [4] => [1,1,1,1] => 4
0001 => [3,1] => [2,1,1] => 3
0010 => [2,1,1] => [3,1] => 2
0011 => [2,2] => [1,2,1] => 2
0100 => [1,1,2] => [1,3] => 2
0101 => [1,1,1,1] => [4] => 1
0110 => [1,2,1] => [2,2] => 2
0111 => [1,3] => [1,1,2] => 3
1000 => [1,3] => [1,1,2] => 3
1001 => [1,2,1] => [2,2] => 2
1010 => [1,1,1,1] => [4] => 1
1011 => [1,1,2] => [1,3] => 2
1100 => [2,2] => [1,2,1] => 2
1101 => [2,1,1] => [3,1] => 2
1110 => [3,1] => [2,1,1] => 3
1111 => [4] => [1,1,1,1] => 4
00000 => [5] => [1,1,1,1,1] => 5
00001 => [4,1] => [2,1,1,1] => 4
00010 => [3,1,1] => [3,1,1] => 3
00011 => [3,2] => [1,2,1,1] => 3
00100 => [2,1,2] => [1,3,1] => 2
00101 => [2,1,1,1] => [4,1] => 2
00110 => [2,2,1] => [2,2,1] => 2
00111 => [2,3] => [1,1,2,1] => 3
01000 => [1,1,3] => [1,1,3] => 3
01001 => [1,1,2,1] => [2,3] => 2
01010 => [1,1,1,1,1] => [5] => 1
01011 => [1,1,1,2] => [1,4] => 2
01100 => [1,2,2] => [1,2,2] => 2
01101 => [1,2,1,1] => [3,2] => 2
01110 => [1,3,1] => [2,1,2] => 3
01111 => [1,4] => [1,1,1,2] => 4
10000 => [1,4] => [1,1,1,2] => 4
10001 => [1,3,1] => [2,1,2] => 3
10010 => [1,2,1,1] => [3,2] => 2
10011 => [1,2,2] => [1,2,2] => 2
10100 => [1,1,1,2] => [1,4] => 2
10101 => [1,1,1,1,1] => [5] => 1
10110 => [1,1,2,1] => [2,3] => 2
10111 => [1,1,3] => [1,1,3] => 3
11000 => [2,3] => [1,1,2,1] => 3
11001 => [2,2,1] => [2,2,1] => 2
11010 => [2,1,1,1] => [4,1] => 2
11011 => [2,1,2] => [1,3,1] => 2
11100 => [3,2] => [1,2,1,1] => 3
11101 => [3,1,1] => [3,1,1] => 3
11110 => [4,1] => [2,1,1,1] => 4
11111 => [5] => [1,1,1,1,1] => 5
000000 => [6] => [1,1,1,1,1,1] => 6
000001 => [5,1] => [2,1,1,1,1] => 5
000010 => [4,1,1] => [3,1,1,1] => 4
000011 => [4,2] => [1,2,1,1,1] => 4
000100 => [3,1,2] => [1,3,1,1] => 3
000101 => [3,1,1,1] => [4,1,1] => 3
000110 => [3,2,1] => [2,2,1,1] => 3
000111 => [3,3] => [1,1,2,1,1] => 3
001000 => [2,1,3] => [1,1,3,1] => 3
001001 => [2,1,2,1] => [2,3,1] => 2
001010 => [2,1,1,1,1] => [5,1] => 2
001011 => [2,1,1,2] => [1,4,1] => 2
001100 => [2,2,2] => [1,2,2,1] => 2
001101 => [2,2,1,1] => [3,2,1] => 2
001110 => [2,3,1] => [2,1,2,1] => 3
001111 => [2,4] => [1,1,1,2,1] => 4
010000 => [1,1,4] => [1,1,1,3] => 4
010001 => [1,1,3,1] => [2,1,3] => 3
010010 => [1,1,2,1,1] => [3,3] => 2
010011 => [1,1,2,2] => [1,2,3] => 2
010100 => [1,1,1,1,2] => [1,5] => 2
010101 => [1,1,1,1,1,1] => [6] => 1
010110 => [1,1,1,2,1] => [2,4] => 2
010111 => [1,1,1,3] => [1,1,4] => 3
011000 => [1,2,3] => [1,1,2,2] => 3
011001 => [1,2,2,1] => [2,2,2] => 2
011010 => [1,2,1,1,1] => [4,2] => 2
011011 => [1,2,1,2] => [1,3,2] => 2
011100 => [1,3,2] => [1,2,1,2] => 3
011101 => [1,3,1,1] => [3,1,2] => 3
011110 => [1,4,1] => [2,1,1,2] => 4
011111 => [1,5] => [1,1,1,1,2] => 5
100000 => [1,5] => [1,1,1,1,2] => 5
100001 => [1,4,1] => [2,1,1,2] => 4
100010 => [1,3,1,1] => [3,1,2] => 3
100011 => [1,3,2] => [1,2,1,2] => 3
100100 => [1,2,1,2] => [1,3,2] => 2
100101 => [1,2,1,1,1] => [4,2] => 2
100110 => [1,2,2,1] => [2,2,2] => 2
>>> Load all 126 entries. <<<
100111 => [1,2,3] => [1,1,2,2] => 3
101000 => [1,1,1,3] => [1,1,4] => 3
101001 => [1,1,1,2,1] => [2,4] => 2
101010 => [1,1,1,1,1,1] => [6] => 1
101011 => [1,1,1,1,2] => [1,5] => 2
101100 => [1,1,2,2] => [1,2,3] => 2
101101 => [1,1,2,1,1] => [3,3] => 2
101110 => [1,1,3,1] => [2,1,3] => 3
101111 => [1,1,4] => [1,1,1,3] => 4
110000 => [2,4] => [1,1,1,2,1] => 4
110001 => [2,3,1] => [2,1,2,1] => 3
110010 => [2,2,1,1] => [3,2,1] => 2
110011 => [2,2,2] => [1,2,2,1] => 2
110100 => [2,1,1,2] => [1,4,1] => 2
110101 => [2,1,1,1,1] => [5,1] => 2
110110 => [2,1,2,1] => [2,3,1] => 2
110111 => [2,1,3] => [1,1,3,1] => 3
111000 => [3,3] => [1,1,2,1,1] => 3
111001 => [3,2,1] => [2,2,1,1] => 3
111010 => [3,1,1,1] => [4,1,1] => 3
111011 => [3,1,2] => [1,3,1,1] => 3
111100 => [4,2] => [1,2,1,1,1] => 4
111101 => [4,1,1] => [3,1,1,1] => 4
111110 => [5,1] => [2,1,1,1,1] => 5
111111 => [6] => [1,1,1,1,1,1] => 6
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The global dimension of the corresponding Comp-Nakayama algebra.
We identify the composition [n1-1,n2-1,...,nr-1] with the Nakayama algebra with Kupisch series [n1,n1-1,...,2,n2,n2-1,...,2,...,nr,nr-1,...,3,2,1]. We call such Nakayama algebras with Kupisch series corresponding to a integer composition "Comp-Nakayama algebra".
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word w is the integer compositions composed of the lengths of consecutive runs of the same letter in w.
Map
conjugate
Description
The conjugate of a composition.
The conjugate of a composition C is defined as the complement (Mp00039complement) of the reversal (Mp00038reverse) of C.
Equivalently, the ribbon shape corresponding to the conjugate of C is the conjugate of the ribbon shape of C.