Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000630
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Mapping
St000630: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1
1 => 1
00 => 1
01 => 2
10 => 2
11 => 1
000 => 1
001 => 2
010 => 1
011 => 2
100 => 2
101 => 1
110 => 2
111 => 1
0000 => 1
0001 => 2
0010 => 2
0011 => 2
0100 => 2
0101 => 2
0110 => 1
0111 => 2
1000 => 2
1001 => 1
1010 => 2
1011 => 2
1100 => 2
1101 => 2
1110 => 2
1111 => 1
00000 => 1
00001 => 2
00010 => 2
00011 => 2
00100 => 1
00101 => 2
00110 => 2
00111 => 2
01000 => 2
01001 => 2
01010 => 1
01011 => 2
01100 => 2
01101 => 2
01110 => 1
01111 => 2
10000 => 2
10001 => 1
10010 => 2
10011 => 2
Description
The length of the shortest palindromic decomposition 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.
Matching statistic: St000526
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000526: Posets ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 40%
Values
0 => [2] => [[2],[]]
 => ([(0,1)],2)
 => 1
1 => [1,1] => [[1,1],[]]
 => ([(0,1)],2)
 => 1
00 => [3] => [[3],[]]
 => ([(0,2),(2,1)],3)
 => 1
01 => [2,1] => [[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => 2
10 => [1,2] => [[2,1],[]]
 => ([(0,1),(0,2)],3)
 => 2
11 => [1,1,1] => [[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => 1
000 => [4] => [[4],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => 1
001 => [3,1] => [[3,3],[2]]
 => ([(0,3),(1,2),(2,3)],4)
 => 2
010 => [2,2] => [[3,2],[1]]
 => ([(0,3),(1,2),(1,3)],4)
 => 1
011 => [2,1,1] => [[2,2,2],[1,1]]
 => ([(0,3),(1,2),(2,3)],4)
 => 2
100 => [1,3] => [[3,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 2
101 => [1,2,1] => [[2,2,1],[1]]
 => ([(0,3),(1,2),(1,3)],4)
 => 1
110 => [1,1,2] => [[2,1,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 2
111 => [1,1,1,1] => [[1,1,1,1],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => 1
0000 => [5] => [[5],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
0001 => [4,1] => [[4,4],[3]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => 2
0010 => [3,2] => [[4,3],[2]]
 => ([(0,3),(1,2),(1,4),(3,4)],5)
 => 2
0011 => [3,1,1] => [[3,3,3],[2,2]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => 2
0100 => [2,3] => [[4,2],[1]]
 => ([(0,4),(1,2),(1,4),(2,3)],5)
 => 2
0101 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
0110 => [2,1,2] => [[3,2,2],[1,1]]
 => ([(0,4),(1,2),(1,3),(3,4)],5)
 => 1
0111 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => 2
1000 => [1,4] => [[4,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 2
1001 => [1,3,1] => [[3,3,1],[2]]
 => ([(0,4),(1,2),(1,3),(3,4)],5)
 => 1
1010 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => 2
1011 => [1,2,1,1] => [[2,2,2,1],[1,1]]
 => ([(0,3),(1,2),(1,4),(3,4)],5)
 => 2
1100 => [1,1,3] => [[3,1,1],[]]
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => 2
1101 => [1,1,2,1] => [[2,2,1,1],[1]]
 => ([(0,4),(1,2),(1,4),(2,3)],5)
 => 2
1110 => [1,1,1,2] => [[2,1,1,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 2
1111 => [1,1,1,1,1] => [[1,1,1,1,1],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
00000 => [6] => [[6],[]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
00001 => [5,1] => [[5,5],[4]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => 2
00010 => [4,2] => [[5,4],[3]]
 => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
 => 2
00011 => [4,1,1] => [[4,4,4],[3,3]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => 2
00100 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => 1
00101 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 2
00110 => [3,1,2] => [[4,3,3],[2,2]]
 => ([(0,4),(1,2),(1,3),(3,5),(4,5)],6)
 => 2
00111 => [3,1,1,1] => [[3,3,3,3],[2,2,2]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => 2
01000 => [2,4] => [[5,2],[1]]
 => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
 => 2
01001 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 2
01010 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => 1
01011 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 2
01100 => [2,1,3] => [[4,2,2],[1,1]]
 => ([(0,5),(1,3),(1,4),(3,5),(4,2)],6)
 => 2
01101 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 2
01110 => [2,1,1,2] => [[3,2,2,2],[1,1,1]]
 => ([(0,5),(1,2),(1,4),(3,5),(4,3)],6)
 => 1
01111 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => 2
10000 => [1,5] => [[5,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 2
10001 => [1,4,1] => [[4,4,1],[3]]
 => ([(0,5),(1,2),(1,4),(3,5),(4,3)],6)
 => 1
10010 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
 => 2
10011 => [1,3,1,1] => [[3,3,3,1],[2,2]]
 => ([(0,4),(1,2),(1,3),(3,5),(4,5)],6)
 => 2
000000 => [7] => [[7],[]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ? = 1
000001 => [6,1] => [[6,6],[5]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 2
000010 => [5,2] => [[6,5],[4]]
 => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ? = 2
000011 => [5,1,1] => [[5,5,5],[4,4]]
 => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
 => ? = 2
000100 => [4,3] => [[6,4],[3]]
 => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
 => ? = 2
000101 => [4,2,1] => [[5,5,4],[4,3]]
 => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7)
 => ? = 2
000110 => [4,1,2] => [[5,4,4],[3,3]]
 => ([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7)
 => ? = 2
000111 => [4,1,1,1] => [[4,4,4,4],[3,3,3]]
 => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
 => ? = 2
001000 => [3,4] => [[6,3],[2]]
 => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7)
 => ? = 2
001001 => [3,3,1] => [[5,5,3],[4,2]]
 => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7)
 => ? = 2
001010 => [3,2,2] => [[5,4,3],[3,2]]
 => ([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7)
 => ? = 2
001011 => [3,2,1,1] => [[4,4,4,3],[3,3,2]]
 => ([(0,5),(0,6),(1,4),(2,3),(3,5),(4,6)],7)
 => ? = 3
001100 => [3,1,3] => [[5,3,3],[2,2]]
 => ([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7)
 => ? = 1
001101 => [3,1,2,1] => [[4,4,3,3],[3,2,2]]
 => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7)
 => ? = 3
001110 => [3,1,1,2] => [[4,3,3,3],[2,2,2]]
 => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7)
 => ? = 2
001111 => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]]
 => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
 => ? = 2
010000 => [2,5] => [[6,2],[1]]
 => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ? = 2
010001 => [2,4,1] => [[5,5,2],[4,1]]
 => ([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7)
 => ? = 2
010010 => [2,3,2] => [[5,4,2],[3,1]]
 => ([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ? = 1
010011 => [2,3,1,1] => [[4,4,4,2],[3,3,1]]
 => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7)
 => ? = 3
010100 => [2,2,3] => [[5,3,2],[2,1]]
 => ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7)
 => ? = 2
010110 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,5),(1,5),(1,6),(2,3),(2,4),(4,6)],7)
 => ? = 3
010111 => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]]
 => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7)
 => ? = 2
011000 => [2,1,4] => [[5,2,2],[1,1]]
 => ([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4)],7)
 => ? = 2
011001 => [2,1,3,1] => [[4,4,2,2],[3,1,1]]
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ? = 3
011010 => [2,1,2,2] => [[4,3,2,2],[2,1,1]]
 => ([(0,6),(1,3),(1,5),(2,4),(2,5),(4,6)],7)
 => ? = 3
011011 => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]]
 => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7)
 => ? = 2
011101 => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]]
 => ([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7)
 => ? = 2
011110 => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]]
 => ([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7)
 => ? = 1
011111 => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 2
100000 => [1,6] => [[6,1],[]]
 => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => ? = 2
100001 => [1,5,1] => [[5,5,1],[4]]
 => ([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7)
 => ? = 1
100010 => [1,4,2] => [[5,4,1],[3]]
 => ([(0,4),(0,6),(1,2),(1,5),(3,6),(5,3)],7)
 => ? = 2
100011 => [1,4,1,1] => [[4,4,4,1],[3,3]]
 => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7)
 => ? = 2
100100 => [1,3,3] => [[5,3,1],[2]]
 => ([(0,5),(0,6),(1,3),(1,4),(4,6),(5,2)],7)
 => ? = 2
100101 => [1,3,2,1] => [[4,4,3,1],[3,2]]
 => ([(0,5),(1,5),(1,6),(2,3),(2,4),(4,6)],7)
 => ? = 3
100110 => [1,3,1,2] => [[4,3,3,1],[2,2]]
 => ([(0,3),(0,5),(1,2),(1,4),(4,6),(5,6)],7)
 => ? = 3
100111 => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]]
 => ([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7)
 => ? = 2
101000 => [1,2,4] => [[5,2,1],[1]]
 => ([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7)
 => ? = 2
101001 => [1,2,3,1] => [[4,4,2,1],[3,1]]
 => ([(0,6),(1,3),(1,5),(2,4),(2,5),(4,6)],7)
 => ? = 3
101010 => [1,2,2,2] => [[4,3,2,1],[2,1]]
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5)],7)
 => ? = 2
101011 => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]]
 => ([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7)
 => ? = 2
101100 => [1,2,1,3] => [[4,2,2,1],[1,1]]
 => ([(0,4),(0,6),(1,3),(1,5),(3,6),(5,2)],7)
 => ? = 3
101101 => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]]
 => ([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
 => ? = 1
101110 => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]]
 => ([(0,4),(0,6),(1,2),(1,5),(3,6),(5,3)],7)
 => ? = 2
101111 => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]]
 => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ? = 2
110000 => [1,1,5] => [[5,1,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ? = 2
110010 => [1,1,3,2] => [[4,3,1,1],[2]]
 => ([(0,4),(0,6),(1,3),(1,5),(3,6),(5,2)],7)
 => ? = 3
110011 => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]]
 => ([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7)
 => ? = 1
110100 => [1,1,2,3] => [[4,2,1,1],[1]]
 => ([(0,5),(0,6),(1,4),(1,6),(4,2),(5,3)],7)
 => ? = 3
Description
The number of posets with combinatorially isomorphic order polytopes.