{"uid":"cap_sqNVXTdfOijyZbChRw3sp","slug":"standard-skew-young-tableau-jeu-de-taquin-rectification-verifier-293a95c1","name":"Standard Skew Young Tableau Jeu de Taquin Rectification Verifier","description":"Verify the entire straight standard tableau obtained by rectifying a supplied skew standard Young 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jeu de taquin rectification on a skew standard Young tableau and verifies the resulting straight standard Young tableau.","exampleAgentPrompt":"Rectify this skew standard Young tableau with outer shape [3,2,1] and inner shape [1] and cells [[1,0,2],[2,1,1],[3,2,0]] using jeu de taquin, and verify that the resulting straight standard Young tableau matches the expected claim.","exampleUseCases":[{"title":"Validate tableau rectification in research","prompt":"I have a skew Young tableau with outer partition [4,3,1], inner partition [2,1], and cell entries [[1,0,3],[2,1,2],[3,2,0],[4,1,1]] — can you apply jeu de taquin rectification and verify the straight standard Young tableau I expect to get?"},{"title":"Check student homework on RSK correspondence","prompt":"My student claims that rectifying the skew tableau with outer shape [3,3,2], inner shape [2,1], and cells [[1,0,2],[2,1,1],[3,2,0]] gives a specific standard Young tableau — can you verify whether that rectification is correct?"},{"title":"Automated combinatorics pipeline validation","prompt":"In my combinatorics pipeline, I need to verify that the jeu de taquin rectification of a skew tableau with outer [5,3,2,1], inner [2,1], and cells [[1,0,4],[2,1,2],[3,2,1],[4,3,0]] produces the claimed straight tableau — can you run the rectification and validate the claim?"}],"resultDescription":"Returns a verification of the full rectified straight standard Young tableau obtained from the supplied skew Young tableau via jeu de taquin slides, along with validation of any provided claim about the rectification outcome.","failureModes":["Invalid skew shape where inner partition does not fit inside outer partition","Cell coordinates outside the skew shape boundaries","Non-standard filling violating the increasing row/column conditions","Outer or inner partition arrays exceeding maximum length of 6","Cells array exceeding maximum of 12 entries","Malformed input JSON missing required fields such as outer, inner, or cells","Claim mismatch returning a validation failure"],"whenToPreferThis":"Use this endpoint when you need to algorithmically rectify a skew standard Young tableau via jeu de taquin and verify the resulting straight tableau, particularly in mathematical research pipelines, combinatorics education tools, or automated theorem-checking systems that require validated RSK-type computations.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:40:30.962Z","isFirstParty":false,"canonicalSlug":"standard-skew-young-tableau-jeu-de-taquin-rectification-verifier-293a95c1"}