A common false belief regarding patience sorting and RSK

The precedure of patience sorting is deceptively similar to the RSK algorithm that one might fathom more is true besides the coincidence about the longest increasing subsequence. For instance, I had always believed that the column sizes of the output from both algorithms match. But the following counterexample flew right into my face:
take the permutation to be 134652, then patience sorting gives
2 5
1 3 4 6
whereas RSK yields the following standard Young tableau

1 2 4 5
It would be interesting to see the what the second and third rows of SYT correspond to in patience sorting.


About aquazorcarson

math PhD at Stanford, studying probability
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