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Matching statistic: St000847
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Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
St000847: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => 1
1 => 1 => 1
00 => 01 => 1
01 => 10 => 1
10 => 11 => 1
11 => 11 => 1
000 => 001 => 1
001 => 010 => 2
010 => 101 => 2
011 => 101 => 2
100 => 101 => 2
101 => 110 => 1
110 => 111 => 1
111 => 111 => 1
0000 => 0001 => 1
0001 => 0010 => 2
0010 => 0101 => 3
0011 => 0101 => 3
0100 => 1001 => 2
0101 => 1010 => 3
0110 => 1011 => 2
0111 => 1011 => 2
1000 => 1001 => 2
1001 => 1010 => 3
1010 => 1101 => 2
1011 => 1101 => 2
1100 => 1101 => 2
1101 => 1110 => 1
1110 => 1111 => 1
1111 => 1111 => 1
00000 => 00001 => 1
00001 => 00010 => 2
00010 => 00101 => 3
00011 => 00101 => 3
00100 => 01001 => 4
00101 => 01010 => 6
00110 => 01011 => 3
00111 => 01011 => 3
01000 => 10001 => 2
01001 => 10010 => 4
01010 => 10101 => 6
01011 => 10101 => 6
01100 => 10101 => 6
01101 => 10110 => 4
01110 => 10111 => 2
01111 => 10111 => 2
10000 => 10001 => 2
10001 => 10010 => 4
10010 => 10101 => 6
10011 => 10101 => 6
Description
The number of standard Young tableaux whose descent set is the binary word. A descent in a standard Young tableau is an entry $i$ such that $i+1$ appears in a lower row in English notation. For example, the tableaux $[[1,2,4],[3]]$ and $[[1,2],[3,4]]$ are those with descent set $\{2\}$, corresponding to the binary word $010$.