Identifier
Values
0 => [2] => [1,1,0,0] => 1
1 => [1,1] => [1,0,1,0] => 2
00 => [3] => [1,1,1,0,0,0] => 1
01 => [2,1] => [1,1,0,0,1,0] => 2
10 => [1,2] => [1,0,1,1,0,0] => 2
11 => [1,1,1] => [1,0,1,0,1,0] => 3
000 => [4] => [1,1,1,1,0,0,0,0] => 1
001 => [3,1] => [1,1,1,0,0,0,1,0] => 2
010 => [2,2] => [1,1,0,0,1,1,0,0] => 2
011 => [2,1,1] => [1,1,0,0,1,0,1,0] => 3
100 => [1,3] => [1,0,1,1,1,0,0,0] => 2
101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
110 => [1,1,2] => [1,0,1,0,1,1,0,0] => 3
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 3
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 4
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 4
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3
11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
11111 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
000011 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3
000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
011100 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
011110 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
>>> Load all 127 entries. <<<
100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
110000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
110111 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4
111000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
111001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
111010 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4
111011 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4
111100 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
111101 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5
111110 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
111111 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
=> [1] => [1,0] => 1
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Description
The finitistic dominant dimension of a Dyck path.
To every LNakayama algebra there is a corresponding Dyck path, see also St000684The global dimension of the LNakayama algebra associated to a Dyck path.. We associate the finitistic dominant dimension of the algebra to the corresponding Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.