Processing math: 100%

Identifier
Values
00 => 01 => 10 => 10 => 1
01 => 10 => 01 => 01 => 1
000 => 001 => 110 => 110 => 1
001 => 010 => 101 => 101 => 2
010 => 101 => 010 => 100 => 1
011 => 101 => 010 => 100 => 1
100 => 101 => 010 => 100 => 1
101 => 110 => 001 => 001 => 1
0000 => 0001 => 1110 => 1110 => 2
0001 => 0010 => 1101 => 1101 => 2
0010 => 0101 => 1010 => 0110 => 2
0011 => 0101 => 1010 => 0110 => 2
0100 => 1001 => 0110 => 1100 => 1
0101 => 1010 => 0101 => 1001 => 2
0110 => 1011 => 0100 => 0100 => 1
0111 => 1011 => 0100 => 0100 => 1
1000 => 1001 => 0110 => 1100 => 1
1001 => 1010 => 0101 => 1001 => 2
1010 => 1101 => 0010 => 1000 => 1
1011 => 1101 => 0010 => 1000 => 1
1100 => 1101 => 0010 => 1000 => 1
1101 => 1110 => 0001 => 0001 => 1
search for individual values
searching the database for the individual values of this statistic
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset.
Let An=K[x]/(xn).
We associate to a nonempty subset S of an (n-1)-set the module MS, which is the direct sum of An-modules with indecomposable non-projective direct summands of dimension i when i is in S (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of MS. We decode the subset as a binary word so that for example the subset S={1,3} of {1,2,3} is decoded as 101.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
Map
valleys-to-peaks
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence 01, or a trailing 0. A peak is a subsequence 10 or a trailing 1. This map replaces every valley with a peak.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00096Foata bijection.