Partitions, Young Tableaux and RSK
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Each question is graded on a single answer: a check that this chapter's methods work, not a test of the reasoning behind them.
How many partitions does have, i.e. what is ?
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comb-enum-101All Combinatorics chaptersAbout these 120 questions
Integer partitions drawn as diagrams, the hook-length formula that counts their standard fillings, and the RSK correspondence. This set covers the chapter Partitions, Young Tableaux and RSK in Combinatorics: 38 easy, 65 medium and 17 hard questions, each graded instantly with a hint and a full step-by-step solution. Progress is saved in this browser only.
- Integer Partitions and Ferrers Diagrams — 10 questions
- Euler's Generating Function for Partitions — 10 questions
- Bijective Proofs for Partition Identities — 10 questions
- Fillings: Semistandard Tableaux and Schur Polynomials — 10 questions
- Standard Young Tableaux — 10 questions
- Hooks, Arms and Legs — 10 questions
- The Hook-Length Formula — 10 questions
- Algorithms that Use the Hook-Length Formula — 10 questions
- A Probabilistic Proof of the Hook-Length Formula — 10 questions
- The RSK Correspondence by Row Insertion — 10 questions
- Schensted's Theorem on Increasing and Decreasing Subsequences — 10 questions
- Symmetry, Involutions and the Sum of Squares — 10 questions