Datasets:

ACDRepo
/

robinson_schensted_knuth_correspondence_10

Formats:

json

Size:

1M - 10M

ArXiv:

Libraries:

Datasets

pandas

License:

Dataset card Data Studio Files Files and versions

xet

Community

Dataset Viewer

Auto-converted to Parquet

Split (2)

train · 2.9M rows

Search is not available for this dataset

Permutation listlengths 10 10	Standard Young tableau 1 listlengths 1 9	Standard Young tableau 2 listlengths 1 9
[ 6, 2, 3, 1, 5, 4, 10, 7, 8, 9 ]	[ [ 1, 3, 4, 7, 8, 9 ], [ 2, 5, 10 ], [ 6 ] ]	[ [ 1, 3, 5, 7, 9, 10 ], [ 2, 6, 8 ], [ 4 ] ]
[ 8, 2, 5, 9, 3, 1, 7, 10, 4, 6 ]	[ [ 1, 3, 4, 6 ], [ 2, 7, 10 ], [ 5, 9 ], [ 8 ] ]	[ [ 1, 3, 4, 8 ], [ 2, 7, 10 ], [ 5, 9 ], [ 6 ] ]
[ 4, 7, 10, 9, 3, 2, 6, 8, 1, 5 ]	[ [ 1, 5, 8 ], [ 2, 6, 9 ], [ 3, 7 ], [ 4 ], [ 10 ] ]	[ [ 1, 2, 3 ], [ 4, 7, 8 ], [ 5, 10 ], [ 6 ], [ 9 ] ]
[ 9, 4, 5, 7, 1, 10, 8, 6, 3, 2 ]	[ [ 1, 2, 6, 8 ], [ 3, 5 ], [ 4, 10 ], [ 7 ], [ 9 ] ]	[ [ 1, 3, 4, 6 ], [ 2, 7 ], [ 5, 8 ], [ 9 ], [ 10 ] ]
[ 8, 1, 6, 3, 7, 2, 10, 9, 4, 5 ]	[ [ 1, 2, 4, 5 ], [ 3, 7, 9 ], [ 6, 10 ], [ 8 ] ]	[ [ 1, 3, 5, 7 ], [ 2, 8, 10 ], [ 4, 9 ], [ 6 ] ]
[ 6, 3, 1, 2, 8, 4, 10, 7, 5, 9 ]	[ [ 1, 2, 4, 5, 9 ], [ 3, 7, 10 ], [ 6, 8 ] ]	[ [ 1, 4, 5, 7, 10 ], [ 2, 6, 8 ], [ 3, 9 ] ]
[ 3, 6, 9, 1, 10, 2, 4, 7, 8, 5 ]	[ [ 1, 2, 4, 5, 8 ], [ 3, 6, 7, 10 ], [ 9 ] ]	[ [ 1, 2, 3, 5, 9 ], [ 4, 6, 7, 8 ], [ 10 ] ]
[ 4, 9, 8, 3, 10, 7, 1, 2, 6, 5 ]	[ [ 1, 2, 5 ], [ 3, 6, 10 ], [ 4, 7 ], [ 8 ], [ 9 ] ]	[ [ 1, 2, 5 ], [ 3, 6, 9 ], [ 4, 8 ], [ 7 ], [ 10 ] ]
[ 5, 1, 7, 8, 4, 3, 10, 6, 2, 9 ]	[ [ 1, 2, 6, 9 ], [ 3, 7, 8, 10 ], [ 4 ], [ 5 ] ]	[ [ 1, 3, 4, 7 ], [ 2, 5, 8, 10 ], [ 6 ], [ 9 ] ]
[ 4, 6, 1, 7, 9, 5, 3, 2, 8, 10 ]	[ [ 1, 2, 7, 8, 10 ], [ 3, 5, 9 ], [ 4 ], [ 6 ] ]	[ [ 1, 2, 4, 5, 10 ], [ 3, 6, 9 ], [ 7 ], [ 8 ] ]
[ 4, 2, 7, 10, 1, 5, 8, 3, 6, 9 ]	[ [ 1, 3, 6, 9 ], [ 2, 5, 8 ], [ 4, 7, 10 ] ]	[ [ 1, 3, 4, 10 ], [ 2, 6, 7 ], [ 5, 8, 9 ] ]
[ 1, 8, 9, 4, 5, 6, 3, 7, 10, 2 ]	[ [ 1, 2, 5, 6, 7, 10 ], [ 3, 9 ], [ 4 ], [ 8 ] ]	[ [ 1, 2, 3, 6, 8, 9 ], [ 4, 5 ], [ 7 ], [ 10 ] ]
[ 3, 4, 5, 9, 7, 6, 1, 10, 2, 8 ]	[ [ 1, 2, 5, 6, 8 ], [ 3, 4, 10 ], [ 7 ], [ 9 ] ]	[ [ 1, 2, 3, 4, 8 ], [ 5, 9, 10 ], [ 6 ], [ 7 ] ]
[ 10, 4, 1, 9, 2, 7, 8, 5, 3, 6 ]	[ [ 1, 2, 3, 6 ], [ 4, 5, 8 ], [ 7 ], [ 9 ], [ 10 ] ]	[ [ 1, 4, 6, 7 ], [ 2, 5, 10 ], [ 3 ], [ 8 ], [ 9 ] ]
[ 10, 5, 9, 2, 8, 4, 6, 3, 7, 1 ]	[ [ 1, 3, 6, 7 ], [ 2, 8 ], [ 4 ], [ 5 ], [ 9 ], [ 10 ] ]	[ [ 1, 3, 7, 9 ], [ 2, 5 ], [ 4 ], [ 6 ], [ 8 ], [ 10 ] ]
[ 4, 2, 6, 10, 9, 5, 7, 1, 8, 3 ]	[ [ 1, 3, 7, 8 ], [ 2, 5, 9 ], [ 4, 6 ], [ 10 ] ]	[ [ 1, 3, 4, 9 ], [ 2, 5, 7 ], [ 6, 10 ], [ 8 ] ]
[ 1, 3, 4, 2, 7, 5, 8, 9, 6, 10 ]	[ [ 1, 2, 4, 5, 6, 9, 10 ], [ 3, 7, 8 ] ]	[ [ 1, 2, 3, 5, 7, 8, 10 ], [ 4, 6, 9 ] ]
[ 10, 1, 4, 8, 2, 7, 6, 5, 3, 9 ]	[ [ 1, 2, 3, 9 ], [ 4, 5 ], [ 6 ], [ 7 ], [ 8 ], [ 10 ] ]	[ [ 1, 3, 4, 10 ], [ 2, 6 ], [ 5 ], [ 7 ], [ 8 ], [ 9 ] ]
[ 7, 5, 10, 2, 6, 4, 8, 9, 1, 3 ]	[ [ 1, 3, 8, 9 ], [ 2, 4 ], [ 5, 6 ], [ 7, 10 ] ]	[ [ 1, 3, 7, 8 ], [ 2, 5 ], [ 4, 6 ], [ 9, 10 ] ]
[ 9, 4, 3, 6, 5, 1, 7, 8, 10, 2 ]	[ [ 1, 2, 7, 8, 10 ], [ 3, 5 ], [ 4, 6 ], [ 9 ] ]	[ [ 1, 4, 7, 8, 9 ], [ 2, 5 ], [ 3, 10 ], [ 6 ] ]
[ 8, 5, 7, 9, 3, 4, 1, 6, 2, 10 ]	[ [ 1, 2, 6, 10 ], [ 3, 4, 9 ], [ 5, 7 ], [ 8 ] ]	[ [ 1, 3, 4, 10 ], [ 2, 6, 8 ], [ 5, 9 ], [ 7 ] ]
[ 3, 7, 6, 9, 2, 1, 10, 5, 4, 8 ]	[ [ 1, 4, 8, 10 ], [ 2, 5, 9 ], [ 3, 6 ], [ 7 ] ]	[ [ 1, 2, 4, 7 ], [ 3, 8, 10 ], [ 5, 9 ], [ 6 ] ]
[ 9, 10, 4, 6, 3, 5, 2, 1, 7, 8 ]	[ [ 1, 5, 7, 8 ], [ 2, 6 ], [ 3, 10 ], [ 4 ], [ 9 ] ]	[ [ 1, 2, 9, 10 ], [ 3, 4 ], [ 5, 6 ], [ 7 ], [ 8 ] ]
[ 1, 6, 10, 5, 7, 9, 8, 4, 3, 2 ]	[ [ 1, 2, 7, 8 ], [ 3, 9 ], [ 4 ], [ 5 ], [ 6 ], [ 10 ] ]	[ [ 1, 2, 3, 6 ], [ 4, 5 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ] ]
[ 9, 8, 7, 4, 3, 5, 2, 10, 6, 1 ]	[ [ 1, 5, 6 ], [ 2, 10 ], [ 3 ], [ 4 ], [ 7 ], [ 8 ], [ 9 ] ]	[ [ 1, 6, 8 ], [ 2, 9 ], [ 3 ], [ 4 ], [ 5 ], [ 7 ], [ 10 ] ]
[ 3, 2, 9, 7, 4, 10, 1, 8, 5, 6 ]	[ [ 1, 4, 5, 6 ], [ 2, 7, 8 ], [ 3, 10 ], [ 9 ] ]	[ [ 1, 3, 6, 10 ], [ 2, 4, 8 ], [ 5, 9 ], [ 7 ] ]
[ 2, 8, 9, 1, 7, 3, 5, 10, 6, 4 ]	[ [ 1, 3, 4, 6 ], [ 2, 5, 9, 10 ], [ 7 ], [ 8 ] ]	[ [ 1, 2, 3, 8 ], [ 4, 5, 7, 9 ], [ 6 ], [ 10 ] ]
[ 10, 4, 1, 3, 6, 2, 5, 9, 7, 8 ]	[ [ 1, 2, 5, 7, 8 ], [ 3, 6, 9 ], [ 4 ], [ 10 ] ]	[ [ 1, 4, 5, 8, 10 ], [ 2, 7, 9 ], [ 3 ], [ 6 ] ]
[ 6, 10, 4, 5, 3, 1, 7, 8, 2, 9 ]	[ [ 1, 2, 7, 8, 9 ], [ 3, 5 ], [ 4, 10 ], [ 6 ] ]	[ [ 1, 2, 7, 8, 10 ], [ 3, 4 ], [ 5, 9 ], [ 6 ] ]
[ 8, 6, 4, 2, 10, 7, 3, 1, 5, 9 ]	[ [ 1, 3, 5, 9 ], [ 2, 7 ], [ 4, 10 ], [ 6 ], [ 8 ] ]	[ [ 1, 5, 9, 10 ], [ 2, 6 ], [ 3, 7 ], [ 4 ], [ 8 ] ]
[ 4, 2, 9, 7, 5, 1, 10, 8, 3, 6 ]	[ [ 1, 3, 6 ], [ 2, 5, 8 ], [ 4, 7, 10 ], [ 9 ] ]	[ [ 1, 3, 7 ], [ 2, 4, 8 ], [ 5, 9, 10 ], [ 6 ] ]
[ 7, 9, 5, 3, 8, 10, 1, 6, 2, 4 ]	[ [ 1, 2, 4 ], [ 3, 6, 10 ], [ 5, 8 ], [ 7, 9 ] ]	[ [ 1, 2, 6 ], [ 3, 5, 10 ], [ 4, 8 ], [ 7, 9 ] ]
[ 6, 2, 7, 8, 5, 10, 4, 1, 9, 3 ]	[ [ 1, 3, 8, 9 ], [ 2, 4, 10 ], [ 5, 7 ], [ 6 ] ]	[ [ 1, 3, 4, 6 ], [ 2, 5, 9 ], [ 7, 10 ], [ 8 ] ]
[ 10, 9, 8, 1, 5, 3, 2, 6, 7, 4 ]	[ [ 1, 2, 4, 7 ], [ 3, 6 ], [ 5 ], [ 8 ], [ 9 ], [ 10 ] ]	[ [ 1, 5, 8, 9 ], [ 2, 10 ], [ 3 ], [ 4 ], [ 6 ], [ 7 ] ]
[ 6, 2, 4, 9, 10, 1, 8, 3, 7, 5 ]	[ [ 1, 3, 5, 10 ], [ 2, 4, 7 ], [ 6, 8 ], [ 9 ] ]	[ [ 1, 3, 4, 5 ], [ 2, 7, 9 ], [ 6, 8 ], [ 10 ] ]
[ 4, 10, 5, 9, 3, 6, 2, 8, 1, 7 ]	[ [ 1, 5, 6, 7 ], [ 2, 8 ], [ 3, 9 ], [ 4 ], [ 10 ] ]	[ [ 1, 2, 4, 8 ], [ 3, 6 ], [ 5, 10 ], [ 7 ], [ 9 ] ]
[ 10, 3, 4, 8, 9, 5, 1, 2, 6, 7 ]	[ [ 1, 2, 5, 6, 7 ], [ 3, 4, 9 ], [ 8 ], [ 10 ] ]	[ [ 1, 3, 4, 5, 10 ], [ 2, 8, 9 ], [ 6 ], [ 7 ] ]
[ 4, 9, 10, 6, 3, 1, 7, 8, 5, 2 ]	[ [ 1, 2, 7, 8 ], [ 3, 5 ], [ 4, 6 ], [ 9, 10 ] ]	[ [ 1, 2, 3, 8 ], [ 4, 7 ], [ 5, 9 ], [ 6, 10 ] ]
[ 9, 7, 2, 6, 10, 3, 1, 5, 4, 8 ]	[ [ 1, 3, 4, 8 ], [ 2, 5 ], [ 6, 10 ], [ 7 ], [ 9 ] ]	[ [ 1, 4, 5, 10 ], [ 2, 8 ], [ 3, 9 ], [ 6 ], [ 7 ] ]
[ 5, 8, 7, 3, 9, 4, 2, 10, 6, 1 ]	[ [ 1, 4, 6, 10 ], [ 2, 7, 9 ], [ 3 ], [ 5 ], [ 8 ] ]	[ [ 1, 2, 5, 8 ], [ 3, 6, 9 ], [ 4 ], [ 7 ], [ 10 ] ]
[ 10, 6, 5, 8, 7, 2, 1, 9, 3, 4 ]	[ [ 1, 3, 4 ], [ 2, 7, 9 ], [ 5, 8 ], [ 6 ], [ 10 ] ]	[ [ 1, 4, 8 ], [ 2, 5, 10 ], [ 3, 9 ], [ 6 ], [ 7 ] ]
[ 10, 3, 8, 6, 4, 1, 5, 9, 7, 2 ]	[ [ 1, 2, 5, 7 ], [ 3, 4 ], [ 6, 9 ], [ 8 ], [ 10 ] ]	[ [ 1, 3, 7, 8 ], [ 2, 9 ], [ 4, 10 ], [ 5 ], [ 6 ] ]
[ 2, 1, 3, 10, 7, 4, 6, 9, 8, 5 ]	[ [ 1, 3, 4, 5, 8 ], [ 2, 6, 9 ], [ 7 ], [ 10 ] ]	[ [ 1, 3, 4, 7, 8 ], [ 2, 5, 9 ], [ 6 ], [ 10 ] ]
[ 6, 5, 4, 10, 9, 1, 3, 2, 8, 7 ]	[ [ 1, 2, 7 ], [ 3, 8 ], [ 4, 9 ], [ 5, 10 ], [ 6 ] ]	[ [ 1, 4, 9 ], [ 2, 5 ], [ 3, 7 ], [ 6, 10 ], [ 8 ] ]
[ 1, 4, 5, 9, 10, 2, 8, 3, 7, 6 ]	[ [ 1, 2, 3, 6, 10 ], [ 4, 5, 7 ], [ 8 ], [ 9 ] ]	[ [ 1, 2, 3, 4, 5 ], [ 6, 7, 9 ], [ 8 ], [ 10 ] ]
[ 1, 10, 7, 3, 9, 6, 4, 8, 5, 2 ]	[ [ 1, 2, 4, 5 ], [ 3, 8 ], [ 6, 9 ], [ 7 ], [ 10 ] ]	[ [ 1, 2, 5, 8 ], [ 3, 6 ], [ 4, 9 ], [ 7 ], [ 10 ] ]
[ 5, 2, 6, 8, 9, 4, 7, 10, 1, 3 ]	[ [ 1, 3, 7, 9, 10 ], [ 2, 4, 8 ], [ 5, 6 ] ]	[ [ 1, 3, 4, 5, 8 ], [ 2, 6, 7 ], [ 9, 10 ] ]
[ 3, 4, 10, 8, 1, 2, 7, 6, 5, 9 ]	[ [ 1, 2, 5, 9 ], [ 3, 4, 6 ], [ 7 ], [ 8 ], [ 10 ] ]	[ [ 1, 2, 3, 10 ], [ 4, 6, 7 ], [ 5 ], [ 8 ], [ 9 ] ]
[ 4, 9, 7, 8, 6, 2, 10, 1, 3, 5 ]	[ [ 1, 3, 5, 10 ], [ 2, 6, 8 ], [ 4 ], [ 7 ], [ 9 ] ]	[ [ 1, 2, 4, 7 ], [ 3, 9, 10 ], [ 5 ], [ 6 ], [ 8 ] ]
[ 2, 10, 9, 5, 1, 6, 8, 3, 7, 4 ]	[ [ 1, 3, 4, 7 ], [ 2, 5, 6 ], [ 8 ], [ 9 ], [ 10 ] ]	[ [ 1, 2, 6, 7 ], [ 3, 8, 9 ], [ 4 ], [ 5 ], [ 10 ] ]
[ 3, 10, 6, 4, 1, 9, 8, 7, 2, 5 ]	[ [ 1, 2, 5 ], [ 3, 4, 7 ], [ 6, 8 ], [ 9 ], [ 10 ] ]	[ [ 1, 2, 6 ], [ 3, 7, 10 ], [ 4, 8 ], [ 5 ], [ 9 ] ]
[ 1, 7, 2, 3, 5, 9, 6, 8, 10, 4 ]	[ [ 1, 2, 3, 4, 6, 8, 10 ], [ 5, 9 ], [ 7 ] ]	[ [ 1, 2, 4, 5, 6, 8, 9 ], [ 3, 7 ], [ 10 ] ]
[ 10, 4, 7, 1, 5, 3, 6, 9, 8, 2 ]	[ [ 1, 2, 6, 8 ], [ 3, 5, 9 ], [ 4 ], [ 7 ], [ 10 ] ]	[ [ 1, 3, 7, 8 ], [ 2, 5, 9 ], [ 4 ], [ 6 ], [ 10 ] ]
[ 10, 6, 3, 8, 5, 2, 4, 1, 9, 7 ]	[ [ 1, 4, 7 ], [ 2, 5, 9 ], [ 3, 8 ], [ 6 ], [ 10 ] ]	[ [ 1, 4, 9 ], [ 2, 5, 10 ], [ 3, 7 ], [ 6 ], [ 8 ] ]
[ 7, 3, 5, 2, 4, 10, 1, 8, 6, 9 ]	[ [ 1, 4, 6, 9 ], [ 2, 5, 8 ], [ 3, 10 ], [ 7 ] ]	[ [ 1, 3, 6, 10 ], [ 2, 5, 8 ], [ 4, 9 ], [ 7 ] ]
[ 9, 7, 2, 1, 3, 5, 8, 10, 4, 6 ]	[ [ 1, 3, 4, 6, 10 ], [ 2, 5, 8 ], [ 7 ], [ 9 ] ]	[ [ 1, 5, 6, 7, 8 ], [ 2, 9, 10 ], [ 3 ], [ 4 ] ]
[ 5, 2, 3, 4, 10, 8, 1, 7, 9, 6 ]	[ [ 1, 3, 4, 6, 9 ], [ 2, 7 ], [ 5, 8 ], [ 10 ] ]	[ [ 1, 3, 4, 5, 9 ], [ 2, 6 ], [ 7, 8 ], [ 10 ] ]
[ 4, 9, 6, 5, 7, 1, 8, 2, 10, 3 ]	[ [ 1, 2, 3, 8, 10 ], [ 4, 5, 7 ], [ 6 ], [ 9 ] ]	[ [ 1, 2, 5, 7, 9 ], [ 3, 8, 10 ], [ 4 ], [ 6 ] ]
[ 1, 10, 2, 5, 8, 9, 6, 7, 4, 3 ]	[ [ 1, 2, 3, 6, 7 ], [ 4, 9 ], [ 5 ], [ 8 ], [ 10 ] ]	[ [ 1, 2, 4, 5, 6 ], [ 3, 8 ], [ 7 ], [ 9 ], [ 10 ] ]
[ 3, 7, 4, 1, 2, 6, 8, 10, 5, 9 ]	[ [ 1, 2, 5, 8, 9 ], [ 3, 4, 6, 10 ], [ 7 ] ]	[ [ 1, 2, 6, 7, 8 ], [ 3, 5, 9, 10 ], [ 4 ] ]
[ 4, 5, 7, 2, 6, 3, 1, 8, 10, 9 ]	[ [ 1, 3, 6, 8, 9 ], [ 2, 5, 10 ], [ 4 ], [ 7 ] ]	[ [ 1, 2, 3, 8, 9 ], [ 4, 5, 10 ], [ 6 ], [ 7 ] ]
[ 9, 7, 5, 8, 4, 10, 2, 6, 1, 3 ]	[ [ 1, 3, 10 ], [ 2, 6 ], [ 4, 8 ], [ 5 ], [ 7 ], [ 9 ] ]	[ [ 1, 4, 6 ], [ 2, 8 ], [ 3, 10 ], [ 5 ], [ 7 ], [ 9 ] ]
[ 5, 9, 8, 2, 1, 10, 7, 4, 6, 3 ]	[ [ 1, 3, 6 ], [ 2, 4, 10 ], [ 5, 7 ], [ 8 ], [ 9 ] ]	[ [ 1, 2, 6 ], [ 3, 7, 9 ], [ 4, 8 ], [ 5 ], [ 10 ] ]
[ 4, 8, 2, 6, 7, 1, 5, 3, 9, 10 ]	[ [ 1, 3, 7, 9, 10 ], [ 2, 5 ], [ 4, 6 ], [ 8 ] ]	[ [ 1, 2, 5, 9, 10 ], [ 3, 4 ], [ 6, 7 ], [ 8 ] ]
[ 5, 1, 10, 6, 2, 3, 4, 9, 8, 7 ]	[ [ 1, 2, 3, 4, 7 ], [ 5, 6, 8 ], [ 9 ], [ 10 ] ]	[ [ 1, 3, 6, 7, 8 ], [ 2, 4, 9 ], [ 5 ], [ 10 ] ]
[ 7, 5, 1, 2, 4, 6, 10, 9, 8, 3 ]	[ [ 1, 2, 3, 6, 8 ], [ 4, 9 ], [ 5, 10 ], [ 7 ] ]	[ [ 1, 4, 5, 6, 7 ], [ 2, 8 ], [ 3, 9 ], [ 10 ] ]
[ 5, 4, 1, 6, 9, 8, 10, 3, 2, 7 ]	[ [ 1, 2, 7, 10 ], [ 3, 6, 8 ], [ 4, 9 ], [ 5 ] ]	[ [ 1, 4, 5, 7 ], [ 2, 6, 10 ], [ 3, 8 ], [ 9 ] ]
[ 10, 6, 2, 3, 1, 4, 8, 5, 7, 9 ]	[ [ 1, 3, 4, 5, 7, 9 ], [ 2, 8 ], [ 6 ], [ 10 ] ]	[ [ 1, 4, 6, 7, 9, 10 ], [ 2, 8 ], [ 3 ], [ 5 ] ]
[ 2, 6, 1, 7, 4, 3, 9, 10, 8, 5 ]	[ [ 1, 3, 5, 8, 10 ], [ 2, 4, 7 ], [ 6, 9 ] ]	[ [ 1, 2, 4, 7, 8 ], [ 3, 5, 9 ], [ 6, 10 ] ]
[ 3, 5, 4, 9, 6, 10, 1, 2, 8, 7 ]	[ [ 1, 2, 6, 7 ], [ 3, 4, 8 ], [ 5, 9, 10 ] ]	[ [ 1, 2, 4, 6 ], [ 3, 5, 9 ], [ 7, 8, 10 ] ]
[ 9, 2, 10, 7, 3, 5, 4, 8, 6, 1 ]	[ [ 1, 3, 4, 6 ], [ 2, 8 ], [ 5, 10 ], [ 7 ], [ 9 ] ]	[ [ 1, 3, 6, 8 ], [ 2, 4 ], [ 5, 9 ], [ 7 ], [ 10 ] ]
[ 10, 4, 9, 6, 7, 2, 3, 5, 1, 8 ]	[ [ 1, 3, 5, 8 ], [ 2, 6, 7 ], [ 4 ], [ 9 ], [ 10 ] ]	[ [ 1, 3, 5, 10 ], [ 2, 7, 8 ], [ 4 ], [ 6 ], [ 9 ] ]
[ 8, 7, 9, 4, 10, 1, 6, 2, 5, 3 ]	[ [ 1, 2, 3 ], [ 4, 5, 10 ], [ 6, 9 ], [ 7 ], [ 8 ] ]	[ [ 1, 3, 5 ], [ 2, 7, 9 ], [ 4, 8 ], [ 6 ], [ 10 ] ]
[ 7, 8, 4, 9, 2, 5, 10, 1, 6, 3 ]	[ [ 1, 3, 6, 10 ], [ 2, 5, 9 ], [ 4, 8 ], [ 7 ] ]	[ [ 1, 2, 4, 7 ], [ 3, 6, 9 ], [ 5, 10 ], [ 8 ] ]
[ 4, 6, 2, 1, 3, 8, 10, 7, 5, 9 ]	[ [ 1, 3, 5, 9 ], [ 2, 6, 7, 10 ], [ 4, 8 ] ]	[ [ 1, 2, 6, 7 ], [ 3, 5, 8, 10 ], [ 4, 9 ] ]
[ 6, 10, 9, 5, 1, 4, 8, 7, 3, 2 ]	[ [ 1, 2, 7 ], [ 3, 8 ], [ 4, 9 ], [ 5 ], [ 6 ], [ 10 ] ]	[ [ 1, 2, 7 ], [ 3, 6 ], [ 4, 8 ], [ 5 ], [ 9 ], [ 10 ] ]
[ 9, 3, 6, 8, 1, 2, 7, 10, 5, 4 ]	[ [ 1, 2, 4, 10 ], [ 3, 5, 7 ], [ 6 ], [ 8 ], [ 9 ] ]	[ [ 1, 3, 4, 8 ], [ 2, 6, 7 ], [ 5 ], [ 9 ], [ 10 ] ]
[ 6, 2, 3, 7, 5, 10, 4, 9, 8, 1 ]	[ [ 1, 3, 4, 8 ], [ 2, 7, 9 ], [ 5, 10 ], [ 6 ] ]	[ [ 1, 3, 4, 6 ], [ 2, 5, 8 ], [ 7, 9 ], [ 10 ] ]
[ 4, 1, 7, 6, 9, 5, 10, 2, 8, 3 ]	[ [ 1, 2, 3, 10 ], [ 4, 5, 8 ], [ 6, 9 ], [ 7 ] ]	[ [ 1, 3, 5, 7 ], [ 2, 4, 9 ], [ 6, 10 ], [ 8 ] ]
[ 8, 1, 10, 3, 9, 2, 6, 4, 5, 7 ]	[ [ 1, 2, 4, 5, 7 ], [ 3, 6 ], [ 8, 9 ], [ 10 ] ]	[ [ 1, 3, 5, 9, 10 ], [ 2, 4 ], [ 6, 7 ], [ 8 ] ]
[ 2, 6, 8, 10, 3, 1, 5, 4, 7, 9 ]	[ [ 1, 3, 4, 7, 9 ], [ 2, 5, 10 ], [ 6, 8 ] ]	[ [ 1, 2, 3, 4, 10 ], [ 5, 7, 9 ], [ 6, 8 ] ]
[ 8, 5, 1, 10, 6, 3, 9, 7, 4, 2 ]	[ [ 1, 2, 4 ], [ 3, 6, 7 ], [ 5, 9 ], [ 8 ], [ 10 ] ]	[ [ 1, 4, 7 ], [ 2, 5, 8 ], [ 3, 6 ], [ 9 ], [ 10 ] ]
[ 7, 10, 9, 4, 3, 1, 8, 6, 5, 2 ]	[ [ 1, 2 ], [ 3, 5 ], [ 4, 6 ], [ 7, 8 ], [ 9 ], [ 10 ] ]	[ [ 1, 2 ], [ 3, 7 ], [ 4, 8 ], [ 5, 9 ], [ 6 ], [ 10 ] ]
[ 10, 6, 1, 3, 7, 4, 2, 9, 5, 8 ]	[ [ 1, 2, 4, 5, 8 ], [ 3, 7, 9 ], [ 6 ], [ 10 ] ]	[ [ 1, 4, 5, 8, 10 ], [ 2, 6, 9 ], [ 3 ], [ 7 ] ]
[ 8, 10, 3, 2, 9, 7, 6, 5, 1, 4 ]	[ [ 1, 4 ], [ 2, 5 ], [ 3, 6 ], [ 7, 9 ], [ 8 ], [ 10 ] ]	[ [ 1, 2 ], [ 3, 5 ], [ 4, 6 ], [ 7, 10 ], [ 8 ], [ 9 ] ]
[ 1, 2, 7, 8, 10, 3, 5, 4, 6, 9 ]	[ [ 1, 2, 3, 4, 6, 9 ], [ 5, 8, 10 ], [ 7 ] ]	[ [ 1, 2, 3, 4, 5, 10 ], [ 6, 7, 9 ], [ 8 ] ]
[ 2, 9, 1, 6, 7, 4, 5, 8, 10, 3 ]	[ [ 1, 3, 5, 8, 10 ], [ 2, 4, 7 ], [ 6 ], [ 9 ] ]	[ [ 1, 2, 5, 8, 9 ], [ 3, 4, 7 ], [ 6 ], [ 10 ] ]
[ 6, 9, 5, 7, 10, 4, 1, 8, 3, 2 ]	[ [ 1, 2, 8 ], [ 3, 7, 10 ], [ 4, 9 ], [ 5 ], [ 6 ] ]	[ [ 1, 2, 5 ], [ 3, 4, 8 ], [ 6, 9 ], [ 7 ], [ 10 ] ]
[ 6, 2, 3, 4, 8, 9, 5, 10, 1, 7 ]	[ [ 1, 3, 4, 5, 7, 10 ], [ 2, 8, 9 ], [ 6 ] ]	[ [ 1, 3, 4, 5, 6, 8 ], [ 2, 7, 10 ], [ 9 ] ]
[ 5, 2, 6, 3, 4, 7, 10, 9, 1, 8 ]	[ [ 1, 3, 4, 7, 8 ], [ 2, 6, 9 ], [ 5, 10 ] ]	[ [ 1, 3, 5, 6, 7 ], [ 2, 4, 8 ], [ 9, 10 ] ]
[ 2, 7, 4, 6, 10, 1, 5, 9, 3, 8 ]	[ [ 1, 3, 5, 8 ], [ 2, 4, 9 ], [ 6, 10 ], [ 7 ] ]	[ [ 1, 2, 4, 5 ], [ 3, 7, 8 ], [ 6, 10 ], [ 9 ] ]
[ 4, 10, 6, 5, 8, 2, 7, 9, 1, 3 ]	[ [ 1, 3, 7, 9 ], [ 2, 5 ], [ 4, 8 ], [ 6 ], [ 10 ] ]	[ [ 1, 2, 5, 8 ], [ 3, 7 ], [ 4, 10 ], [ 6 ], [ 9 ] ]
[ 7, 9, 5, 2, 4, 10, 8, 6, 1, 3 ]	[ [ 1, 3, 6 ], [ 2, 4, 10 ], [ 5, 8 ], [ 7, 9 ] ]	[ [ 1, 2, 6 ], [ 3, 5, 7 ], [ 4, 8 ], [ 9, 10 ] ]
[ 9, 6, 10, 8, 1, 2, 5, 3, 7, 4 ]	[ [ 1, 2, 3, 4 ], [ 5, 7 ], [ 6, 8 ], [ 9, 10 ] ]	[ [ 1, 3, 7, 9 ], [ 2, 4 ], [ 5, 6 ], [ 8, 10 ] ]
[ 4, 9, 5, 2, 10, 6, 1, 8, 7, 3 ]	[ [ 1, 3, 6, 7 ], [ 2, 5 ], [ 4, 8 ], [ 9, 10 ] ]	[ [ 1, 2, 5, 8 ], [ 3, 6 ], [ 4, 9 ], [ 7, 10 ] ]
[ 1, 6, 5, 3, 10, 8, 2, 7, 4, 9 ]	[ [ 1, 2, 4, 9 ], [ 3, 7 ], [ 5, 8 ], [ 6, 10 ] ]	[ [ 1, 2, 5, 10 ], [ 3, 6 ], [ 4, 8 ], [ 7, 9 ] ]
[ 2, 6, 8, 10, 5, 7, 4, 9, 3, 1 ]	[ [ 1, 3, 7, 9 ], [ 2, 8, 10 ], [ 4 ], [ 5 ], [ 6 ] ]	[ [ 1, 2, 3, 4 ], [ 5, 6, 8 ], [ 7 ], [ 9 ], [ 10 ] ]
[ 3, 4, 8, 5, 1, 7, 2, 6, 9, 10 ]	[ [ 1, 2, 5, 6, 9, 10 ], [ 3, 4, 7 ], [ 8 ] ]	[ [ 1, 2, 3, 6, 9, 10 ], [ 4, 7, 8 ], [ 5 ] ]
[ 9, 1, 10, 2, 6, 5, 4, 3, 8, 7 ]	[ [ 1, 2, 3, 7 ], [ 4, 8 ], [ 5, 10 ], [ 6 ], [ 9 ] ]	[ [ 1, 3, 5, 9 ], [ 2, 4 ], [ 6, 10 ], [ 7 ], [ 8 ] ]
[ 9, 4, 7, 2, 8, 3, 5, 1, 10, 6 ]	[ [ 1, 3, 5, 6 ], [ 2, 7, 8, 10 ], [ 4 ], [ 9 ] ]	[ [ 1, 3, 5, 9 ], [ 2, 6, 7, 10 ], [ 4 ], [ 8 ] ]

End of preview. Expand in Data Studio

The Robinson-Schensted-Knuth Correspondence for Permutations of Size 10

The Robinson-Schensted-Knuth (RSK) algorithm [1,2] gives a bijection between pairs of semistandard Young tableau of the same shape and matrices with non-negative integer entries. The special case we consider (which is sometimes called the Robinson-Schensted algorithm) restricts to a bijection between pairs of standard Young tableaux and permutations in $S_{n}$ . This correspondence is highly significant in algebraic combinatorics because it connects two of the most fundamental objects in the field, permutations and standard Young tableaux.

The goal of this dataset is to see whether a model can learn the RSK algorithm. That is, for a fixed $n$ the model is provided with a pair of standard Young tableaux $\lambda_1, \lambda_2$ of size $n$ and required to predict the corresponding permutation (note that the RSK algorithm is usually introduced as a map from permutations to pairs of standard Young tableaux but we have found that it is easier to design neural architectures that output permutations and have hence reversed the bijection for this dataset). Although the algorithm is known, it would be significant for a model to learn this correspondence due to the the intricate combinatorial rules involved. Notably, the RSK correspondence can be used to find the length of the longest increasing subsequence of a permutation, so a model that learns this algorithm implicitly must also learn to solve the increasing subsequence problem. Additionally, given the numerous generalizations of the RSK correspondence, a model that performs well on this task could potentially be investigated for its ability to generalize to other related combinatorial settings.

Dataset

The dataset consists of triples: two standard Young tableaux of size $n$ and their corresponding permutation (obtained via the RSK algorithm). Standard Young tableaux are written as a list of lists so that [ [ 1, 4, 7 ], [ 2, 6, 8 ], [ 3 ], [ 5 ] ] is a tableaux of shape $(3, 3, 1, 1)$ whose first row has entries 1, 4, 7.

Unlike some of the other datasets where permutations are written in 1-line notation, in this dataset we write permutations in terms of their inversion set. For a permutation $\sigma$ on $n$ elements, the inversion set gives all pairs of integers $1 \leq i < j \leq n$ such that $\sigma(j) < \sigma(i)$ . There are $\binom{n}{2}$ possible inversions for $\sigma$ . We represent the inversion set as a binary code where $1$ means that $\sigma$ inverts $(i, j)$ and $0$ means that it does not. Note that an inversion set completely characterizes a permutation.

The entries of the inversion vector are written in lexicographical order. The lexicographical order on transpositions of the set $\{1, 2, 3\}$ is $(1, 2)$ , $(1, 3)$ , $(2, 3)$ . Since the permutation $213$ inverts $(1, 2)$ but not $(1, 3)$ or $(2, 3)$ , its binary code would be written as 1, 0, 0.

Data generation

This dataset was generated with Sage [3]. Code can be found here.

Task

ML task: Given a pair of standard Young tableaux, predict the corresponding permutation obtained via the RSK algorithm. As noted above, output permutations are represented as a ${0, 1}$ -vector corresponding to their inversion set.

While the RSK algorithm is simple enough to be taught to a grade school student, it may involve many steps for larger $n$ . This may be the ultimate reason this is a hard problem for ML algorithms.

Further information

Curated by: Helen Jenne
Funded by: Pacific Northwest National Laboratory
Language(s) (NLP): NA
License: CC-by-2.0

Dataset Sources

The dataset was generated using SageMath. Data generation scripts can be found here.

Repository: ACD Repo

Citation

BibTeX:

@article{chau2025machine,
    title={Machine learning meets algebraic combinatorics: A suite of datasets capturing research-level conjecturing ability in pure mathematics},
    author={Chau, Herman and Jenne, Helen and Brown, Davis and He, Jesse and Raugas, Mark and Billey, Sara and Kvinge, Henry},
    journal={arXiv preprint arXiv:2503.06366},
    year={2025}
}

APA:

Chau, H., Jenne, H., Brown, D., He, J., Raugas, M., Billey, S., & Kvinge, H. (2025). Machine learning meets algebraic combinatorics: A suite of datasets capturing research-level conjecturing ability in pure mathematics. arXiv preprint arXiv:2503.06366.

Dataset Card Contact

Henry Kvinge, [email protected]

References

[1] Robinson, G. de B. "On the representations of the symmetric group." American Journal of Mathematics (1938): 745-760.
[2] Schensted, Craige. "Longest increasing and decreasing subsequences." Canadian Journal of mathematics 13 (1961): 179-191.
[3] Stein, William. "Sage: Open source mathematical software." (2008).

Downloads last month: 38

Size of downloaded dataset files:

683 MB

Size of the auto-converted Parquet files:

71.7 MB

Number of rows:

3,628,800