Identifier
-
Mp00097:
Binary words
—delta morphism⟶
Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001239: Dyck paths ⟶ ℤ
Values
0 => [1] => [1,0] => 1
1 => [1] => [1,0] => 1
00 => [2] => [1,1,0,0] => 1
01 => [1,1] => [1,0,1,0] => 2
10 => [1,1] => [1,0,1,0] => 2
11 => [2] => [1,1,0,0] => 1
000 => [3] => [1,1,1,0,0,0] => 1
001 => [2,1] => [1,1,0,0,1,0] => 2
010 => [1,1,1] => [1,0,1,0,1,0] => 2
011 => [1,2] => [1,0,1,1,0,0] => 2
100 => [1,2] => [1,0,1,1,0,0] => 2
101 => [1,1,1] => [1,0,1,0,1,0] => 2
110 => [2,1] => [1,1,0,0,1,0] => 2
111 => [3] => [1,1,1,0,0,0] => 1
0000 => [4] => [1,1,1,1,0,0,0,0] => 1
0001 => [3,1] => [1,1,1,0,0,0,1,0] => 2
0010 => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
0011 => [2,2] => [1,1,0,0,1,1,0,0] => 2
0100 => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
0111 => [1,3] => [1,0,1,1,1,0,0,0] => 2
1000 => [1,3] => [1,0,1,1,1,0,0,0] => 2
1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
1011 => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
1100 => [2,2] => [1,1,0,0,1,1,0,0] => 2
1101 => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
1110 => [3,1] => [1,1,1,0,0,0,1,0] => 2
1111 => [4] => [1,1,1,1,0,0,0,0] => 1
00000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
00010 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
00100 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
00101 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
01000 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
01001 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
01010 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
01011 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
01101 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
10010 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
10100 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
10101 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
10110 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
10111 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
11010 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
11011 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
11101 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
11110 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
11111 => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
000001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
000010 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
000011 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
000100 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
000101 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
000110 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
000111 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
001000 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
001001 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
001010 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
001011 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
001100 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
001101 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
001110 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
001111 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
010000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
010001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
010010 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
010011 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
010100 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
010101 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 2
010110 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
010111 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
011000 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
011010 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
011011 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
011100 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
011101 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
011110 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
011111 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
100000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
100010 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
100011 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
100100 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
100101 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
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Description
The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra.
Map
bounce path
Description
The bounce path determined by an integer composition.
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 $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
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