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Matching statistic: St001916
Mapping
St001916: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0
1 => 0
00 => 0
01 => 0
10 => 0
11 => 2
000 => 2
001 => 2
010 => 2
011 => 4
100 => 2
101 => 4
110 => 4
111 => 10
0000 => 10
0001 => 11
0010 => 11
0011 => 11
0100 => 11
0101 => 5
0110 => 11
0111 => 26
1000 => 11
1001 => 11
1010 => 5
1011 => 26
1100 => 11
1101 => 26
1110 => 26
1111 => 41
00000 => 41
00001 => 51
00010 => 51
00011 => 40
00100 => 51
00101 => 27
00110 => 40
00111 => 62
01000 => 51
01001 => 27
01010 => 27
01011 => 29
01100 => 40
01101 => 29
01110 => 62
01111 => 130
10000 => 51
10001 => 40
10010 => 27
10011 => 62
Description
The number of transient elements in the orbit of Bulgarian solitaire corresponding to a necklace. A move in Bulgarian solitaire consists of removing the first column of the Ferrers diagram and inserting it as a new row. The connected components of the corresponding discrete dynamical system are indexed by necklaces in a natural way. The binary words corresponding to a necklace index the recurrent elements in a component, the remaining elements are called transient.