Identifier
Values
{{1}} => [1] => [1,0] => 0
{{1,2}} => [2] => [1,1,0,0] => 0
{{1},{2}} => [1,1] => [1,0,1,0] => 0
{{1,2,3}} => [3] => [1,1,1,0,0,0] => 0
{{1,2},{3}} => [2,1] => [1,1,0,0,1,0] => 0
{{1,3},{2}} => [2,1] => [1,1,0,0,1,0] => 0
{{1},{2,3}} => [1,2] => [1,0,1,1,0,0] => 0
{{1},{2},{3}} => [1,1,1] => [1,0,1,0,1,0] => 0
{{1,2,3,4}} => [4] => [1,1,1,1,0,0,0,0] => 0
{{1,2,3},{4}} => [3,1] => [1,1,1,0,0,0,1,0] => 0
{{1,2,4},{3}} => [3,1] => [1,1,1,0,0,0,1,0] => 0
{{1,2},{3,4}} => [2,2] => [1,1,0,0,1,1,0,0] => 0
{{1,2},{3},{4}} => [2,1,1] => [1,1,0,0,1,0,1,0] => 0
{{1,3,4},{2}} => [3,1] => [1,1,1,0,0,0,1,0] => 0
{{1,3},{2,4}} => [2,2] => [1,1,0,0,1,1,0,0] => 0
{{1,3},{2},{4}} => [2,1,1] => [1,1,0,0,1,0,1,0] => 0
{{1,4},{2,3}} => [2,2] => [1,1,0,0,1,1,0,0] => 0
{{1},{2,3,4}} => [1,3] => [1,0,1,1,1,0,0,0] => 0
{{1},{2,3},{4}} => [1,2,1] => [1,0,1,1,0,0,1,0] => 0
{{1,4},{2},{3}} => [2,1,1] => [1,1,0,0,1,0,1,0] => 0
{{1},{2,4},{3}} => [1,2,1] => [1,0,1,1,0,0,1,0] => 0
{{1},{2},{3,4}} => [1,1,2] => [1,0,1,0,1,1,0,0] => 0
{{1},{2},{3},{4}} => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
{{1,2,3,4,5}} => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
{{1,2,3,4},{5}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
{{1,2,3,5},{4}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
{{1,2,3},{4,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
{{1,2,3},{4},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
{{1,2,4,5},{3}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
{{1,2,4},{3,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
{{1,2,4},{3},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
{{1,2,5},{3,4}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
{{1,2},{3,4,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 0
{{1,2},{3,4},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
{{1,2,5},{3},{4}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
{{1,2},{3,5},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
{{1,2},{3},{4,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 0
{{1,2},{3},{4},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
{{1,3,4,5},{2}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
{{1,3,4},{2,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
{{1,3,4},{2},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
{{1,3,5},{2,4}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
{{1,3},{2,4,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 0
{{1,3},{2,4},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
{{1,3,5},{2},{4}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
{{1,3},{2,5},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
{{1,3},{2},{4,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 0
{{1,3},{2},{4},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
{{1,4,5},{2,3}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
{{1,4},{2,3,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 0
{{1,4},{2,3},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
{{1,5},{2,3,4}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 0
{{1},{2,3,4,5}} => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1},{2,3,4},{5}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
{{1,5},{2,3},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
{{1},{2,3,5},{4}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
{{1},{2,3},{4,5}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
{{1},{2,3},{4},{5}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 0
{{1,4,5},{2},{3}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
{{1,4},{2,5},{3}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
{{1,4},{2},{3,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 0
{{1,4},{2},{3},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
{{1,5},{2,4},{3}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
{{1},{2,4,5},{3}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
{{1},{2,4},{3,5}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
{{1},{2,4},{3},{5}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 0
{{1,5},{2},{3,4}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 0
{{1},{2,5},{3,4}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
{{1},{2},{3,4,5}} => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 0
{{1},{2},{3,4},{5}} => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 0
{{1,5},{2},{3},{4}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
{{1},{2,5},{3},{4}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 0
{{1},{2},{3,5},{4}} => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 0
{{1},{2},{3},{4,5}} => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 0
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
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Description
The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to composition
Description
The integer composition of block sizes of a set partition.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.