Abstract
We view the RSK correspondence as associating to each permutation π∈Sn a Young diagram λ=λ(π), i.e. a partition of n. Suppose now that π is left-multiplied by t transpositions, what is the largest number of cells in λ that can change as a result? It is natural refer to this question as the search for the Lipschitz constant of the RSK correspondence.We show upper bounds on this Lipschitz constant as a function of t. For t= 1, we give a construction of permutations that achieve this bound exactly. For larger t we construct permutations which come close to matching the upper bound that we prove.
Original language | English |
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Pages (from-to) | 63-82 |
Number of pages | 20 |
Journal | Journal of Combinatorial Theory. Series A |
Volume | 119 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2012 |
Keywords
- Lipschitz constant
- RSK correspondence
- Transpositions
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics