On the Lipschitz constant of the RSK correspondence

Nayantara Bhatnagar*, Nathan Linial

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageAmerican English
Pages (from-to)63-82
Number of pages20
JournalJournal of Combinatorial Theory. Series A
Volume119
Issue number1
DOIs
StatePublished - Jan 2012

Keywords

  • Lipschitz constant
  • RSK correspondence
  • Transpositions

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