Identifier
Images
=>
Cc0007;cc-rep-0Cc0018;cc-rep-1Cc0018;cc-rep-2Cc0019;cc-rep-3
[[1]]=>[[1]]=>[[1]]=>[[1]]=>[1] [[1,2]]=>[[2,0],[1]]=>[[2,0],[1]]=>[[1,2]]=>[1,2] [[1],[2]]=>[[1,1],[1]]=>[[1,1],[1]]=>[[1],[2]]=>[2,1] [[1,2,3]]=>[[3,0,0],[2,0],[1]]=>[[3,0,0],[2,0],[1]]=>[[1,2,3]]=>[1,2,3] [[1,3],[2]]=>[[2,1,0],[1,1],[1]]=>[[2,1,0],[2,0],[1]]=>[[1,2],[3]]=>[3,1,2] [[1,2],[3]]=>[[2,1,0],[2,0],[1]]=>[[2,1,0],[1,1],[1]]=>[[1,3],[2]]=>[2,1,3] [[1],[2],[3]]=>[[1,1,1],[1,1],[1]]=>[[1,1,1],[1,1],[1]]=>[[1],[2],[3]]=>[3,2,1] [[1,2,3,4]]=>[[4,0,0,0],[3,0,0],[2,0],[1]]=>[[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4]]=>[1,2,3,4] [[1,3,4],[2]]=>[[3,1,0,0],[2,1,0],[1,1],[1]]=>[[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3]]=>[3,1,2,4] [[1,2,4],[3]]=>[[3,1,0,0],[2,1,0],[2,0],[1]]=>[[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4]]=>[4,1,2,3] [[1,2,3],[4]]=>[[3,1,0,0],[3,0,0],[2,0],[1]]=>[[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4],[2]]=>[2,1,3,4] [[1,3],[2,4]]=>[[2,2,0,0],[2,1,0],[1,1],[1]]=>[[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,4]]=>[3,4,1,2] [[1,2],[3,4]]=>[[2,2,0,0],[2,1,0],[2,0],[1]]=>[[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,4]]=>[2,4,1,3] [[1,4],[2],[3]]=>[[2,1,1,0],[1,1,1],[1,1],[1]]=>[[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4]]=>[4,3,1,2] [[1,3],[2],[4]]=>[[2,1,1,0],[2,1,0],[1,1],[1]]=>[[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2],[3]]=>[3,2,1,4] [[1,2],[3],[4]]=>[[2,1,1,0],[2,1,0],[2,0],[1]]=>[[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2],[4]]=>[4,2,1,3] [[1],[2],[3],[4]]=>[[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1],[2],[3],[4]]=>[4,3,2,1] [[1,2,3,4,5]]=>[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5]]=>[1,2,3,4,5] [[1,3,4,5],[2]]=>[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3]]=>[3,1,2,4,5] [[1,2,4,5],[3]]=>[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4]]=>[4,1,2,3,5] [[1,2,3,5],[4]]=>[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5]]=>[5,1,2,3,4] [[1,2,3,4],[5]]=>[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4,5],[2]]=>[2,1,3,4,5] [[1,3,5],[2,4]]=>[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5]]=>[3,5,1,2,4] [[1,2,5],[3,4]]=>[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4,5]]=>[4,5,1,2,3] [[1,3,4],[2,5]]=>[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,4]]=>[3,4,1,2,5] [[1,2,4],[3,5]]=>[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3,5],[2,4]]=>[2,4,1,3,5] [[1,2,3],[4,5]]=>[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4],[2,5]]=>[2,5,1,3,4] [[1,4,5],[2],[3]]=>[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3],[4]]=>[4,3,1,2,5] [[1,3,5],[2],[4]]=>[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3],[5]]=>[5,3,1,2,4] [[1,2,5],[3],[4]]=>[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5]]=>[5,4,1,2,3] [[1,3,4],[2],[5]]=>[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4,5],[2],[3]]=>[3,2,1,4,5] [[1,2,4],[3],[5]]=>[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3,5],[2],[4]]=>[4,2,1,3,5] [[1,2,3],[4],[5]]=>[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4],[2],[5]]=>[5,2,1,3,4] [[1,4],[2,5],[3]]=>[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,5],[4]]=>[4,3,5,1,2] [[1,3],[2,5],[4]]=>[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,4],[5]]=>[5,3,4,1,2] [[1,2],[3,5],[4]]=>[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,4],[5]]=>[5,2,4,1,3] [[1,3],[2,4],[5]]=>[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2,5],[3]]=>[3,2,5,1,4] [[1,2],[3,4],[5]]=>[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,5],[4]]=>[4,2,5,1,3] [[1,5],[2],[3],[4]]=>[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5]]=>[5,4,3,1,2] [[1,4],[2],[3],[5]]=>[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,5],[2],[3],[4]]=>[4,3,2,1,5] [[1,3],[2],[4],[5]]=>[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2],[3],[5]]=>[5,3,2,1,4] [[1,2],[3],[4],[5]]=>[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2],[4],[5]]=>[5,4,2,1,3] [[1],[2],[3],[4],[5]]=>[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1],[2],[3],[4],[5]]=>[5,4,3,2,1] [[1,2,3,4,5,6]]=>[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6] [[1,3,4,5,6],[2]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6] [[1,2,4,5,6],[3]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6] [[1,2,3,5,6],[4]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6] [[1,2,3,4,6],[5]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5] [[1,2,3,4,5],[6]]=>[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6] [[1,3,5,6],[2,4]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6] [[1,2,5,6],[3,4]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6] [[1,3,4,6],[2,5]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5] [[1,2,4,6],[3,5]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5] [[1,2,3,6],[4,5]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4] [[1,3,4,5],[2,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6] [[1,2,4,5],[3,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6] [[1,2,3,5],[4,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6] [[1,2,3,4],[5,6]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5] [[1,4,5,6],[2],[3]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6] [[1,3,5,6],[2],[4]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6] [[1,2,5,6],[3],[4]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6] [[1,3,4,6],[2],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5] [[1,2,4,6],[3],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5] [[1,2,3,6],[4],[5]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4] [[1,3,4,5],[2],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6] [[1,2,4,5],[3],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6] [[1,2,3,5],[4],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6] [[1,2,3,4],[5],[6]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5] [[1,3,5],[2,4,6]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4] [[1,2,5],[3,4,6]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3] [[1,3,4],[2,5,6]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5] [[1,2,4],[3,5,6]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5] [[1,2,3],[4,5,6]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4] [[1,4,6],[2,5],[3]]=>[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5] [[1,3,6],[2,5],[4]]=>[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4] [[1,2,6],[3,5],[4]]=>[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3] [[1,3,6],[2,4],[5]]=>[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4] [[1,2,6],[3,4],[5]]=>[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3] [[1,4,5],[2,6],[3]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6] [[1,3,5],[2,6],[4]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6] [[1,2,5],[3,6],[4]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6] [[1,3,4],[2,6],[5]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5] [[1,2,4],[3,6],[5]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5] [[1,2,3],[4,6],[5]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4] [[1,3,5],[2,4],[6]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6] [[1,2,5],[3,4],[6]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6] [[1,3,4],[2,5],[6]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5] [[1,2,4],[3,5],[6]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5] [[1,2,3],[4,5],[6]]=>[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4] [[1,5,6],[2],[3],[4]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6] [[1,4,6],[2],[3],[5]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5] [[1,3,6],[2],[4],[5]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4] [[1,2,6],[3],[4],[5]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3] [[1,4,5],[2],[3],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6] [[1,3,5],[2],[4],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6] [[1,2,5],[3],[4],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6] [[1,3,4],[2],[5],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5] [[1,2,4],[3],[5],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5] [[1,2,3],[4],[5],[6]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4] [[1,4],[2,5],[3,6]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2] [[1,3],[2,5],[4,6]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2] [[1,2],[3,5],[4,6]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3] [[1,3],[2,4],[5,6]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4] [[1,2],[3,4],[5,6]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3] [[1,5],[2,6],[3],[4]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2] [[1,4],[2,6],[3],[5]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2] [[1,3],[2,6],[4],[5]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2] [[1,2],[3,6],[4],[5]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3] [[1,4],[2,5],[3],[6]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5] [[1,3],[2,5],[4],[6]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4] [[1,2],[3,5],[4],[6]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3] [[1,3],[2,4],[5],[6]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4] [[1,2],[3,4],[5],[6]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3] [[1,6],[2],[3],[4],[5]]=>[[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2] [[1,5],[2],[3],[4],[6]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6] [[1,4],[2],[3],[5],[6]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5] [[1,3],[2],[4],[5],[6]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4] [[1,2],[3],[4],[5],[6]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3] [[1],[2],[3],[4],[5],[6]]=>[[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]
Map
to Gelfand-Tsetlin pattern
Description
Sends a tableau to its corresponding Gelfand-Tsetlin pattern.
To obtain this Gelfand-Tsetlin pattern, fill in the first row of the pattern with the shape of the tableau.
Then remove the maximal entry from the tableau to obtain a smaller tableau, and repeat the process until the tableau is empty.
Map
promotion
Description
The promotion of a Gelfand-Tsetlin pattern.
Gelfand-Tsetlin patterns are in bijection with pairs consisting of an integer $m$ and a semistandard Young tableau whose maximal entry is at most $m$. Sch├╝tzenberger's promotion operator is a bijection on this set. Additionally it preserves the shape of the tableau, which corresponds to the first row of the pattern.
Map
to semistandard tableau
Description
Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$ \lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)}, $$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).