Identifier
- St000290: Binary words ⟶ ℤ
Values
=>
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10111011100000=>15
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1111011100000010=>27
1111101010000010=>36
1111101100000010=>28
1111110001000010=>31
1111110010000010=>30
1111110100000010=>29
1111111000000010=>22
111111110000000010=>25
101111111100000000=>11
111111101000000010=>33
101111111010000000=>21
111111100100000010=>34
111111011000000010=>32
101111111001000000=>22
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11111111100000000010=>28
10111111111000000000=>12
11111111010000000010=>37
10111111110100000000=>23
1111111111000000000010=>31
1011111111110000000000=>13
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Description
The major index of a binary word.
This is the sum of the positions of descents, i.e., a one followed by a zero.
For words of length $n$ with $a$ zeros, the generating function for the major index is the $q$-binomial coefficient $\binom{n}{a}_q$.
This is the sum of the positions of descents, i.e., a one followed by a zero.
For words of length $n$ with $a$ zeros, the generating function for the major index is the $q$-binomial coefficient $\binom{n}{a}_q$.
Code
def statistic(x): return x.major_index()
Created
Nov 19, 2015 at 11:57 by Martin Rubey
Updated
Nov 17, 2019 at 18:31 by Martin Rubey
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