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Matching statistic: St000631
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Mapping
St000631: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1
1 => 1
00 => 2
01 => 1
10 => 1
11 => 2
000 => 4
001 => 2
010 => 2
011 => 2
100 => 2
101 => 2
110 => 2
111 => 4
0000 => 8
0001 => 4
0010 => 3
0011 => 4
0100 => 3
0101 => 3
0110 => 3
0111 => 4
1000 => 4
1001 => 3
1010 => 3
1011 => 3
1100 => 4
1101 => 3
1110 => 4
1111 => 8
00000 => 16
00001 => 8
00010 => 6
00011 => 8
00100 => 6
00101 => 5
00110 => 5
00111 => 8
01000 => 6
01001 => 4
01010 => 5
01011 => 5
01100 => 5
01101 => 4
01110 => 5
01111 => 8
10000 => 8
10001 => 5
10010 => 4
10011 => 5
Description
The number of distinct palindromic decompositions of a binary word. A palindromic decomposition (paldec for short) of a word $w=a_1,\dots,a_n$ is any list of factors $p_1,\dots,p_k$ such that $w=p_1\dots p_k$ and each $p_i$ is a palindrome, i.e. coincides with itself read backwards.