Identifier
Values
[2,1] => 01 => 10 => 01 => 1
[2,2] => 00 => 01 => 10 => 1
[2,1,1] => 011 => 101 => 010 => 1
[4,1] => 01 => 10 => 01 => 1
[2,2,1] => 001 => 010 => 101 => 2
[2,1,1,1] => 0111 => 1011 => 0100 => 1
[4,2] => 00 => 01 => 10 => 1
[4,1,1] => 011 => 101 => 010 => 1
[3,2,1] => 101 => 110 => 001 => 1
[2,2,2] => 000 => 001 => 110 => 1
[2,2,1,1] => 0011 => 0101 => 1010 => 0
[6,1] => 01 => 10 => 01 => 1
[4,3] => 01 => 10 => 01 => 1
[4,2,1] => 001 => 010 => 101 => 2
[4,1,1,1] => 0111 => 1011 => 0100 => 1
[3,2,2] => 100 => 101 => 010 => 1
[3,2,1,1] => 1011 => 1101 => 0010 => 1
[2,2,2,1] => 0001 => 0010 => 1101 => 2
[6,2] => 00 => 01 => 10 => 1
[6,1,1] => 011 => 101 => 010 => 1
[5,2,1] => 101 => 110 => 001 => 1
[4,4] => 00 => 01 => 10 => 1
[4,3,1] => 011 => 101 => 010 => 1
[4,2,2] => 000 => 001 => 110 => 1
[4,2,1,1] => 0011 => 0101 => 1010 => 0
[3,2,2,1] => 1001 => 1010 => 0101 => 0
[2,2,2,2] => 0000 => 0001 => 1110 => 2
[8,1] => 01 => 10 => 01 => 1
[6,3] => 01 => 10 => 01 => 1
[6,2,1] => 001 => 010 => 101 => 2
[6,1,1,1] => 0111 => 1011 => 0100 => 1
[5,2,2] => 100 => 101 => 010 => 1
[5,2,1,1] => 1011 => 1101 => 0010 => 1
[4,4,1] => 001 => 010 => 101 => 2
[4,3,2] => 010 => 101 => 010 => 1
[4,3,1,1] => 0111 => 1011 => 0100 => 1
[4,2,2,1] => 0001 => 0010 => 1101 => 2
[3,3,2,1] => 1101 => 1110 => 0001 => 1
[3,2,2,2] => 1000 => 1001 => 0110 => 2
[8,2] => 00 => 01 => 10 => 1
[8,1,1] => 011 => 101 => 010 => 1
[7,2,1] => 101 => 110 => 001 => 1
[6,4] => 00 => 01 => 10 => 1
[6,3,1] => 011 => 101 => 010 => 1
[6,2,2] => 000 => 001 => 110 => 1
[6,2,1,1] => 0011 => 0101 => 1010 => 0
[5,4,1] => 101 => 110 => 001 => 1
[5,2,2,1] => 1001 => 1010 => 0101 => 0
[4,4,2] => 000 => 001 => 110 => 1
[4,4,1,1] => 0011 => 0101 => 1010 => 0
[4,3,3] => 011 => 101 => 010 => 1
[4,3,2,1] => 0101 => 1010 => 0101 => 0
[4,2,2,2] => 0000 => 0001 => 1110 => 2
[3,3,2,2] => 1100 => 1101 => 0010 => 1
[10,1] => 01 => 10 => 01 => 1
[8,3] => 01 => 10 => 01 => 1
[8,2,1] => 001 => 010 => 101 => 2
[8,1,1,1] => 0111 => 1011 => 0100 => 1
[7,2,2] => 100 => 101 => 010 => 1
[7,2,1,1] => 1011 => 1101 => 0010 => 1
[6,5] => 01 => 10 => 01 => 1
[6,4,1] => 001 => 010 => 101 => 2
[6,3,2] => 010 => 101 => 010 => 1
[6,3,1,1] => 0111 => 1011 => 0100 => 1
[6,2,2,1] => 0001 => 0010 => 1101 => 2
[5,4,2] => 100 => 101 => 010 => 1
[5,4,1,1] => 1011 => 1101 => 0010 => 1
[5,3,2,1] => 1101 => 1110 => 0001 => 1
[5,2,2,2] => 1000 => 1001 => 0110 => 2
[4,4,3] => 001 => 010 => 101 => 2
[4,4,2,1] => 0001 => 0010 => 1101 => 2
[4,3,3,1] => 0111 => 1011 => 0100 => 1
[4,3,2,2] => 0100 => 1001 => 0110 => 2
[10,2] => 00 => 01 => 10 => 1
[10,1,1] => 011 => 101 => 010 => 1
[9,2,1] => 101 => 110 => 001 => 1
[8,4] => 00 => 01 => 10 => 1
[8,3,1] => 011 => 101 => 010 => 1
[8,2,2] => 000 => 001 => 110 => 1
[8,2,1,1] => 0011 => 0101 => 1010 => 0
[7,4,1] => 101 => 110 => 001 => 1
[7,2,2,1] => 1001 => 1010 => 0101 => 0
[6,6] => 00 => 01 => 10 => 1
[6,5,1] => 011 => 101 => 010 => 1
[6,4,2] => 000 => 001 => 110 => 1
[6,4,1,1] => 0011 => 0101 => 1010 => 0
[6,3,3] => 011 => 101 => 010 => 1
[6,3,2,1] => 0101 => 1010 => 0101 => 0
[6,2,2,2] => 0000 => 0001 => 1110 => 2
[5,4,3] => 101 => 110 => 001 => 1
[5,4,2,1] => 1001 => 1010 => 0101 => 0
[5,3,2,2] => 1100 => 1101 => 0010 => 1
[4,4,4] => 000 => 001 => 110 => 1
[4,4,3,1] => 0011 => 0101 => 1010 => 0
[4,4,2,2] => 0000 => 0001 => 1110 => 2
[4,3,3,2] => 0110 => 1011 => 0100 => 1
[12,1] => 01 => 10 => 01 => 1
[10,3] => 01 => 10 => 01 => 1
[10,2,1] => 001 => 010 => 101 => 2
[10,1,1,1] => 0111 => 1011 => 0100 => 1
[9,2,2] => 100 => 101 => 010 => 1
>>> Load all 301 entries. <<<
[9,2,1,1] => 1011 => 1101 => 0010 => 1
[8,5] => 01 => 10 => 01 => 1
[8,4,1] => 001 => 010 => 101 => 2
[8,3,2] => 010 => 101 => 010 => 1
[8,3,1,1] => 0111 => 1011 => 0100 => 1
[8,2,2,1] => 0001 => 0010 => 1101 => 2
[7,4,2] => 100 => 101 => 010 => 1
[7,4,1,1] => 1011 => 1101 => 0010 => 1
[7,3,2,1] => 1101 => 1110 => 0001 => 1
[7,2,2,2] => 1000 => 1001 => 0110 => 2
[6,6,1] => 001 => 010 => 101 => 2
[6,5,2] => 010 => 101 => 010 => 1
[6,5,1,1] => 0111 => 1011 => 0100 => 1
[6,4,3] => 001 => 010 => 101 => 2
[6,4,2,1] => 0001 => 0010 => 1101 => 2
[6,3,3,1] => 0111 => 1011 => 0100 => 1
[6,3,2,2] => 0100 => 1001 => 0110 => 2
[5,5,2,1] => 1101 => 1110 => 0001 => 1
[5,4,4] => 100 => 101 => 010 => 1
[5,4,3,1] => 1011 => 1101 => 0010 => 1
[5,4,2,2] => 1000 => 1001 => 0110 => 2
[4,4,4,1] => 0001 => 0010 => 1101 => 2
[4,4,3,2] => 0010 => 0101 => 1010 => 0
[4,3,3,3] => 0111 => 1011 => 0100 => 1
[12,2] => 00 => 01 => 10 => 1
[12,1,1] => 011 => 101 => 010 => 1
[11,2,1] => 101 => 110 => 001 => 1
[10,4] => 00 => 01 => 10 => 1
[10,3,1] => 011 => 101 => 010 => 1
[10,2,2] => 000 => 001 => 110 => 1
[10,2,1,1] => 0011 => 0101 => 1010 => 0
[9,4,1] => 101 => 110 => 001 => 1
[9,2,2,1] => 1001 => 1010 => 0101 => 0
[8,6] => 00 => 01 => 10 => 1
[8,5,1] => 011 => 101 => 010 => 1
[8,4,2] => 000 => 001 => 110 => 1
[8,4,1,1] => 0011 => 0101 => 1010 => 0
[8,3,3] => 011 => 101 => 010 => 1
[8,3,2,1] => 0101 => 1010 => 0101 => 0
[8,2,2,2] => 0000 => 0001 => 1110 => 2
[7,6,1] => 101 => 110 => 001 => 1
[7,4,3] => 101 => 110 => 001 => 1
[7,4,2,1] => 1001 => 1010 => 0101 => 0
[7,3,2,2] => 1100 => 1101 => 0010 => 1
[6,6,2] => 000 => 001 => 110 => 1
[6,6,1,1] => 0011 => 0101 => 1010 => 0
[6,5,3] => 011 => 101 => 010 => 1
[6,5,2,1] => 0101 => 1010 => 0101 => 0
[6,4,4] => 000 => 001 => 110 => 1
[6,4,3,1] => 0011 => 0101 => 1010 => 0
[6,4,2,2] => 0000 => 0001 => 1110 => 2
[6,3,3,2] => 0110 => 1011 => 0100 => 1
[5,5,2,2] => 1100 => 1101 => 0010 => 1
[5,4,4,1] => 1001 => 1010 => 0101 => 0
[5,4,3,2] => 1010 => 1101 => 0010 => 1
[4,4,4,2] => 0000 => 0001 => 1110 => 2
[4,4,3,3] => 0011 => 0101 => 1010 => 0
[14,1] => 01 => 10 => 01 => 1
[12,3] => 01 => 10 => 01 => 1
[12,2,1] => 001 => 010 => 101 => 2
[12,1,1,1] => 0111 => 1011 => 0100 => 1
[11,2,2] => 100 => 101 => 010 => 1
[11,2,1,1] => 1011 => 1101 => 0010 => 1
[10,5] => 01 => 10 => 01 => 1
[10,4,1] => 001 => 010 => 101 => 2
[10,3,2] => 010 => 101 => 010 => 1
[10,3,1,1] => 0111 => 1011 => 0100 => 1
[10,2,2,1] => 0001 => 0010 => 1101 => 2
[9,4,2] => 100 => 101 => 010 => 1
[9,4,1,1] => 1011 => 1101 => 0010 => 1
[9,3,2,1] => 1101 => 1110 => 0001 => 1
[9,2,2,2] => 1000 => 1001 => 0110 => 2
[8,7] => 01 => 10 => 01 => 1
[8,6,1] => 001 => 010 => 101 => 2
[8,5,2] => 010 => 101 => 010 => 1
[8,5,1,1] => 0111 => 1011 => 0100 => 1
[8,4,3] => 001 => 010 => 101 => 2
[8,4,2,1] => 0001 => 0010 => 1101 => 2
[8,3,3,1] => 0111 => 1011 => 0100 => 1
[8,3,2,2] => 0100 => 1001 => 0110 => 2
[7,6,2] => 100 => 101 => 010 => 1
[7,6,1,1] => 1011 => 1101 => 0010 => 1
[7,5,2,1] => 1101 => 1110 => 0001 => 1
[7,4,4] => 100 => 101 => 010 => 1
[7,4,3,1] => 1011 => 1101 => 0010 => 1
[7,4,2,2] => 1000 => 1001 => 0110 => 2
[6,6,3] => 001 => 010 => 101 => 2
[6,6,2,1] => 0001 => 0010 => 1101 => 2
[6,5,4] => 010 => 101 => 010 => 1
[6,5,3,1] => 0111 => 1011 => 0100 => 1
[6,5,2,2] => 0100 => 1001 => 0110 => 2
[6,4,4,1] => 0001 => 0010 => 1101 => 2
[6,4,3,2] => 0010 => 0101 => 1010 => 0
[6,3,3,3] => 0111 => 1011 => 0100 => 1
[5,5,4,1] => 1101 => 1110 => 0001 => 1
[5,4,4,2] => 1000 => 1001 => 0110 => 2
[5,4,3,3] => 1011 => 1101 => 0010 => 1
[4,4,4,3] => 0001 => 0010 => 1101 => 2
[14,2] => 00 => 01 => 10 => 1
[14,1,1] => 011 => 101 => 010 => 1
[13,2,1] => 101 => 110 => 001 => 1
[12,4] => 00 => 01 => 10 => 1
[12,3,1] => 011 => 101 => 010 => 1
[12,2,2] => 000 => 001 => 110 => 1
[12,2,1,1] => 0011 => 0101 => 1010 => 0
[11,4,1] => 101 => 110 => 001 => 1
[11,2,2,1] => 1001 => 1010 => 0101 => 0
[10,6] => 00 => 01 => 10 => 1
[10,5,1] => 011 => 101 => 010 => 1
[10,4,2] => 000 => 001 => 110 => 1
[10,4,1,1] => 0011 => 0101 => 1010 => 0
[10,3,3] => 011 => 101 => 010 => 1
[10,3,2,1] => 0101 => 1010 => 0101 => 0
[10,2,2,2] => 0000 => 0001 => 1110 => 2
[9,6,1] => 101 => 110 => 001 => 1
[9,4,3] => 101 => 110 => 001 => 1
[9,4,2,1] => 1001 => 1010 => 0101 => 0
[9,3,2,2] => 1100 => 1101 => 0010 => 1
[8,8] => 00 => 01 => 10 => 1
[8,7,1] => 011 => 101 => 010 => 1
[8,6,2] => 000 => 001 => 110 => 1
[8,6,1,1] => 0011 => 0101 => 1010 => 0
[8,5,3] => 011 => 101 => 010 => 1
[8,5,2,1] => 0101 => 1010 => 0101 => 0
[8,4,4] => 000 => 001 => 110 => 1
[8,4,3,1] => 0011 => 0101 => 1010 => 0
[8,4,2,2] => 0000 => 0001 => 1110 => 2
[8,3,3,2] => 0110 => 1011 => 0100 => 1
[7,6,3] => 101 => 110 => 001 => 1
[7,6,2,1] => 1001 => 1010 => 0101 => 0
[7,5,2,2] => 1100 => 1101 => 0010 => 1
[7,4,4,1] => 1001 => 1010 => 0101 => 0
[7,4,3,2] => 1010 => 1101 => 0010 => 1
[6,6,4] => 000 => 001 => 110 => 1
[6,6,3,1] => 0011 => 0101 => 1010 => 0
[6,6,2,2] => 0000 => 0001 => 1110 => 2
[6,5,5] => 011 => 101 => 010 => 1
[6,5,4,1] => 0101 => 1010 => 0101 => 0
[6,5,3,2] => 0110 => 1011 => 0100 => 1
[6,4,4,2] => 0000 => 0001 => 1110 => 2
[6,4,3,3] => 0011 => 0101 => 1010 => 0
[5,5,4,2] => 1100 => 1101 => 0010 => 1
[5,4,4,3] => 1001 => 1010 => 0101 => 0
[4,4,4,4] => 0000 => 0001 => 1110 => 2
[16,1] => 01 => 10 => 01 => 1
[14,3] => 01 => 10 => 01 => 1
[14,2,1] => 001 => 010 => 101 => 2
[14,1,1,1] => 0111 => 1011 => 0100 => 1
[13,2,2] => 100 => 101 => 010 => 1
[13,2,1,1] => 1011 => 1101 => 0010 => 1
[12,5] => 01 => 10 => 01 => 1
[12,4,1] => 001 => 010 => 101 => 2
[12,3,2] => 010 => 101 => 010 => 1
[12,3,1,1] => 0111 => 1011 => 0100 => 1
[12,2,2,1] => 0001 => 0010 => 1101 => 2
[11,4,2] => 100 => 101 => 010 => 1
[11,4,1,1] => 1011 => 1101 => 0010 => 1
[11,3,2,1] => 1101 => 1110 => 0001 => 1
[11,2,2,2] => 1000 => 1001 => 0110 => 2
[10,7] => 01 => 10 => 01 => 1
[10,6,1] => 001 => 010 => 101 => 2
[10,5,2] => 010 => 101 => 010 => 1
[10,5,1,1] => 0111 => 1011 => 0100 => 1
[10,4,3] => 001 => 010 => 101 => 2
[10,4,2,1] => 0001 => 0010 => 1101 => 2
[10,3,3,1] => 0111 => 1011 => 0100 => 1
[10,3,2,2] => 0100 => 1001 => 0110 => 2
[9,6,2] => 100 => 101 => 010 => 1
[9,6,1,1] => 1011 => 1101 => 0010 => 1
[9,5,2,1] => 1101 => 1110 => 0001 => 1
[9,4,4] => 100 => 101 => 010 => 1
[9,4,3,1] => 1011 => 1101 => 0010 => 1
[9,4,2,2] => 1000 => 1001 => 0110 => 2
[8,8,1] => 001 => 010 => 101 => 2
[8,7,2] => 010 => 101 => 010 => 1
[8,7,1,1] => 0111 => 1011 => 0100 => 1
[8,6,3] => 001 => 010 => 101 => 2
[8,6,2,1] => 0001 => 0010 => 1101 => 2
[8,5,4] => 010 => 101 => 010 => 1
[8,5,3,1] => 0111 => 1011 => 0100 => 1
[8,5,2,2] => 0100 => 1001 => 0110 => 2
[8,4,4,1] => 0001 => 0010 => 1101 => 2
[8,4,3,2] => 0010 => 0101 => 1010 => 0
[8,3,3,3] => 0111 => 1011 => 0100 => 1
[7,7,2,1] => 1101 => 1110 => 0001 => 1
[7,6,4] => 100 => 101 => 010 => 1
[7,6,3,1] => 1011 => 1101 => 0010 => 1
[7,6,2,2] => 1000 => 1001 => 0110 => 2
[7,5,4,1] => 1101 => 1110 => 0001 => 1
[7,4,4,2] => 1000 => 1001 => 0110 => 2
[7,4,3,3] => 1011 => 1101 => 0010 => 1
[6,6,5] => 001 => 010 => 101 => 2
[6,6,4,1] => 0001 => 0010 => 1101 => 2
[6,6,3,2] => 0010 => 0101 => 1010 => 0
[6,5,5,1] => 0111 => 1011 => 0100 => 1
[6,5,4,2] => 0100 => 1001 => 0110 => 2
[6,5,3,3] => 0111 => 1011 => 0100 => 1
[6,4,4,3] => 0001 => 0010 => 1101 => 2
[5,5,4,3] => 1101 => 1110 => 0001 => 1
[5,4,4,4] => 1000 => 1001 => 0110 => 2
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 $A_n=K[x]/(x^n)$.
We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-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 $M_S$. 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
odd parts
Description
Return the binary word indicating which parts of the partition are odd.
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.