Processing math: 100%

Identifier
Values
[1] => 10 => 01 => 10 => 1
[2] => 100 => 001 => 110 => 1
[1,1] => 110 => 011 => 100 => 1
[3] => 1000 => 0001 => 1110 => 2
[2,1] => 1010 => 0011 => 1100 => 1
[1,1,1] => 1110 => 0111 => 1000 => 1
[2,2] => 1100 => 0011 => 1100 => 1
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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
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
Map
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.