{"id":16698840,"url":"https://github.com/stla/standardyoungtableaux.jl","last_synced_at":"2026-05-19T17:41:10.939Z","repository":{"id":46169212,"uuid":"326208450","full_name":"stla/StandardYoungTableaux.jl","owner":"stla","description":"Standard Young 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StandardYoungTableaux\n\n[![Build Status](https://github.com/stla/StandardYoungTableaux.jl/workflows/CI/badge.svg)](https://github.com/stla/StandardYoungTableaux.jl/actions)\n\n- All standard Young tableaux of a given shape:\n\n```julia\njulia\u003e lambda = IPartition([3, 1])\nIPartition(4, [3, 1])\n\njulia\u003e allSYTx(lambda)\n3-element Vector{StandardYoungTableau}:\n StandardYoungTableau(IPartition(4, [3, 1]), [[1, 3, 4], [2]])\n StandardYoungTableau(IPartition(4, [3, 1]), [[1, 2, 4], [3]])\n StandardYoungTableau(IPartition(4, [3, 1]), [[1, 2, 3], [4]])\n```\n\n- Count of all standard Young tableaux of a given shape:\n\n```julia\njulia\u003e lambda = IPartition([4, 2])\nIPartition(6, [4, 2])\n\njulia\u003e countSYTx(lambda)\n9\n```\n\n- Uniform sampling of standard Young tableaux:\n\n```julia\njulia\u003e randomSYT(lambda)\nStandardYoungTableau(IPartition(6, [4, 2]), [[1, 2, 3, 6], [4, 5]])\n```\n\n- Robinson-Schensted(-Knuth) correspondence:\n\n```julia\njulia\u003e P, Q = RS([3, 4, 1, 2])\n(P = StandardYoungTableau(IPartition(4, [2, 2]), [[1, 2], [3, 4]]), Q = StandardYoungTableau(IPartition(4, [2, 2]), [[1, 2], [3, 4]]))\n\njulia\u003e P\nStandardYoungTableau(IPartition(4, [2, 2]), [[1, 2], [3, 4]])\n\njulia\u003e Q\nStandardYoungTableau(IPartition(4, [2, 2]), [[1, 2], [3, 4]])\n```\n\n- Conversion to and from paths of integer partitions on the Young graph:\n\n```julia\njulia\u003e y = StandardYoungTableau([[1,3,4], [2]])\nStandardYoungTableau(IPartition(4, [3, 1]), [[1, 3, 4], [2]])\n\njulia\u003e path = SYT2YoungPath(y)\n4-element Vector{IPartition}:\n IPartition(1, [1])\n IPartition(2, [1, 1])\n IPartition(3, [2, 1])\n IPartition(4, [3, 1])\n\njulia\u003e YoungPath2SYT(path)\nStandardYoungTableau(IPartition(4, [3, 1]), [[1, 3, 4], [2]])\n```\n\n\u003cimg src=\"http://stla.github.io/stlapblog/posts/assets/img/young_yng_path.png\" width=\"400\" /\u003e\n\n- Plancherel growth process:\n\n```julia\njulia\u003e path = randomYoungPath(5)\n5-element Vector{IPartition}:\n IPartition(1, [1])\n IPartition(2, [2])\n IPartition(3, [2, 1])\n IPartition(4, [3, 1])\n IPartition(5, [3, 1, 1])\n\njulia\u003e YoungPath2SYT(path)\nStandardYoungTableau(IPartition(5, [3, 1, 1]), [[1, 2, 4], [3], [5]])\n```\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstla%2Fstandardyoungtableaux.jl","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstla%2Fstandardyoungtableaux.jl","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstla%2Fstandardyoungtableaux.jl/lists"}