Identifier
Values
{{1}} => [1] => [[1],[]] => ([],1) => 0
{{1,2}} => [2] => [[2],[]] => ([(0,1)],2) => 0
{{1},{2}} => [1,1] => [[1,1],[]] => ([(0,1)],2) => 0
{{1,2,3}} => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 0
{{1,2},{3}} => [2,1] => [[2,2],[1]] => ([(0,2),(1,2)],3) => 0
{{1,3},{2}} => [2,1] => [[2,2],[1]] => ([(0,2),(1,2)],3) => 0
{{1},{2,3}} => [1,2] => [[2,1],[]] => ([(0,1),(0,2)],3) => 0
{{1},{2},{3}} => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 0
{{1,2,3,4}} => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 0
{{1,2,3},{4}} => [3,1] => [[3,3],[2]] => ([(0,3),(1,2),(2,3)],4) => 0
{{1,2,4},{3}} => [3,1] => [[3,3],[2]] => ([(0,3),(1,2),(2,3)],4) => 0
{{1,2},{3,4}} => [2,2] => [[3,2],[1]] => ([(0,3),(1,2),(1,3)],4) => 0
{{1,2},{3},{4}} => [2,1,1] => [[2,2,2],[1,1]] => ([(0,3),(1,2),(2,3)],4) => 0
{{1,3,4},{2}} => [3,1] => [[3,3],[2]] => ([(0,3),(1,2),(2,3)],4) => 0
{{1,3},{2,4}} => [2,2] => [[3,2],[1]] => ([(0,3),(1,2),(1,3)],4) => 0
{{1,3},{2},{4}} => [2,1,1] => [[2,2,2],[1,1]] => ([(0,3),(1,2),(2,3)],4) => 0
{{1,4},{2,3}} => [2,2] => [[3,2],[1]] => ([(0,3),(1,2),(1,3)],4) => 0
{{1},{2,3,4}} => [1,3] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 0
{{1},{2,3},{4}} => [1,2,1] => [[2,2,1],[1]] => ([(0,3),(1,2),(1,3)],4) => 0
{{1,4},{2},{3}} => [2,1,1] => [[2,2,2],[1,1]] => ([(0,3),(1,2),(2,3)],4) => 0
{{1},{2,4},{3}} => [1,2,1] => [[2,2,1],[1]] => ([(0,3),(1,2),(1,3)],4) => 0
{{1},{2},{3,4}} => [1,1,2] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 0
{{1},{2},{3},{4}} => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 0
{{1,2,3,4,5}} => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
{{1,2,3,4},{5}} => [4,1] => [[4,4],[3]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
{{1,2,3,5},{4}} => [4,1] => [[4,4],[3]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
{{1,2,3},{4,5}} => [3,2] => [[4,3],[2]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 0
{{1,2,3},{4},{5}} => [3,1,1] => [[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 0
{{1,2,4,5},{3}} => [4,1] => [[4,4],[3]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
{{1,2,4},{3,5}} => [3,2] => [[4,3],[2]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 0
{{1,2,4},{3},{5}} => [3,1,1] => [[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 0
{{1,2,5},{3,4}} => [3,2] => [[4,3],[2]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 0
{{1,2},{3,4,5}} => [2,3] => [[4,2],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => 0
{{1,2},{3,4},{5}} => [2,2,1] => [[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
{{1,2,5},{3},{4}} => [3,1,1] => [[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 0
{{1,2},{3,5},{4}} => [2,2,1] => [[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
{{1,2},{3},{4,5}} => [2,1,2] => [[3,2,2],[1,1]] => ([(0,4),(1,2),(1,3),(3,4)],5) => 0
{{1,2},{3},{4},{5}} => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
{{1,3,4,5},{2}} => [4,1] => [[4,4],[3]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
{{1,3,4},{2,5}} => [3,2] => [[4,3],[2]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 0
{{1,3,4},{2},{5}} => [3,1,1] => [[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 0
{{1,3,5},{2,4}} => [3,2] => [[4,3],[2]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 0
{{1,3},{2,4,5}} => [2,3] => [[4,2],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => 0
{{1,3},{2,4},{5}} => [2,2,1] => [[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
{{1,3,5},{2},{4}} => [3,1,1] => [[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 0
{{1,3},{2,5},{4}} => [2,2,1] => [[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
{{1,3},{2},{4,5}} => [2,1,2] => [[3,2,2],[1,1]] => ([(0,4),(1,2),(1,3),(3,4)],5) => 0
{{1,3},{2},{4},{5}} => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
{{1,4,5},{2,3}} => [3,2] => [[4,3],[2]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 0
{{1,4},{2,3,5}} => [2,3] => [[4,2],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => 0
{{1,4},{2,3},{5}} => [2,2,1] => [[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
{{1,5},{2,3,4}} => [2,3] => [[4,2],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => 0
{{1},{2,3,4,5}} => [1,4] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 0
{{1},{2,3,4},{5}} => [1,3,1] => [[3,3,1],[2]] => ([(0,4),(1,2),(1,3),(3,4)],5) => 0
{{1,5},{2,3},{4}} => [2,2,1] => [[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
{{1},{2,3,5},{4}} => [1,3,1] => [[3,3,1],[2]] => ([(0,4),(1,2),(1,3),(3,4)],5) => 0
{{1},{2,3},{4,5}} => [1,2,2] => [[3,2,1],[1]] => ([(0,3),(0,4),(1,2),(1,4)],5) => 0
{{1},{2,3},{4},{5}} => [1,2,1,1] => [[2,2,2,1],[1,1]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 0
{{1,4,5},{2},{3}} => [3,1,1] => [[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 0
{{1,4},{2,5},{3}} => [2,2,1] => [[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
{{1,4},{2},{3,5}} => [2,1,2] => [[3,2,2],[1,1]] => ([(0,4),(1,2),(1,3),(3,4)],5) => 0
{{1,4},{2},{3},{5}} => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
{{1,5},{2,4},{3}} => [2,2,1] => [[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
{{1},{2,4,5},{3}} => [1,3,1] => [[3,3,1],[2]] => ([(0,4),(1,2),(1,3),(3,4)],5) => 0
{{1},{2,4},{3,5}} => [1,2,2] => [[3,2,1],[1]] => ([(0,3),(0,4),(1,2),(1,4)],5) => 0
{{1},{2,4},{3},{5}} => [1,2,1,1] => [[2,2,2,1],[1,1]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 0
{{1,5},{2},{3,4}} => [2,1,2] => [[3,2,2],[1,1]] => ([(0,4),(1,2),(1,3),(3,4)],5) => 0
{{1},{2,5},{3,4}} => [1,2,2] => [[3,2,1],[1]] => ([(0,3),(0,4),(1,2),(1,4)],5) => 0
{{1},{2},{3,4,5}} => [1,1,3] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 0
{{1},{2},{3,4},{5}} => [1,1,2,1] => [[2,2,1,1],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => 0
{{1,5},{2},{3},{4}} => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
{{1},{2,5},{3},{4}} => [1,2,1,1] => [[2,2,2,1],[1,1]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 0
{{1},{2},{3,5},{4}} => [1,1,2,1] => [[2,2,1,1],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => 0
{{1},{2},{3},{4,5}} => [1,1,1,2] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 0
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
{{1,2,3,4,5,6}} => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
{{1,2,3,4,5},{6}} => [5,1] => [[5,5],[4]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
{{1,2,3,4,6},{5}} => [5,1] => [[5,5],[4]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
{{1,2,3,4},{5},{6}} => [4,1,1] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,2,3,5,6},{4}} => [5,1] => [[5,5],[4]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
{{1,2,3,5},{4},{6}} => [4,1,1] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,2,3},{4,5},{6}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,2,3,6},{4},{5}} => [4,1,1] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,2,3},{4,6},{5}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,2,4,5,6},{3}} => [5,1] => [[5,5],[4]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
{{1,2,4,5},{3},{6}} => [4,1,1] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,2,4},{3,5},{6}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,2,4,6},{3},{5}} => [4,1,1] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,2,4},{3,6},{5}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,2,5},{3,4},{6}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,2,6},{3,4},{5}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,2},{3,4},{5},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,2,5,6},{3},{4}} => [4,1,1] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,2,5},{3,6},{4}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,2,6},{3,5},{4}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,2},{3,5},{4},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,2},{3,6},{4},{5}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
>>> Load all 142 entries. <<<
{{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
{{1,3,4,5,6},{2}} => [5,1] => [[5,5],[4]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
{{1,3,4,5},{2},{6}} => [4,1,1] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,3,4},{2,5},{6}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,3,4,6},{2},{5}} => [4,1,1] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,3,4},{2,6},{5}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,3,5},{2,4},{6}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,3,6},{2,4},{5}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,3},{2,4},{5},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,3,5,6},{2},{4}} => [4,1,1] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,3,5},{2,6},{4}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,3,6},{2,5},{4}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,3},{2,5},{4},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,3},{2,6},{4},{5}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
{{1,4,5},{2,3},{6}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,4,6},{2,3},{5}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,4},{2,3},{5},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,5,6},{2,3},{4}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,5},{2,3},{4},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,6},{2,3},{4},{5}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,4,5,6},{2},{3}} => [4,1,1] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,4,5},{2,6},{3}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,4,6},{2,5},{3}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,4},{2,5},{3},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,4},{2,6},{3},{5}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
{{1,5,6},{2,4},{3}} => [3,2,1] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,5},{2,4},{3},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,6},{2,4},{3},{5}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
{{1,5},{2,6},{3},{4}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
{{1,6},{2,5},{3},{4}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 0
{{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
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Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
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to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
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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.
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cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.