TY - JOUR

T1 - On the Lipschitz constant of the RSK correspondence

AU - Bhatnagar, Nayantara

AU - Linial, Nathan

PY - 2012/1

Y1 - 2012/1

N2 - 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.

AB - 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.

KW - Lipschitz constant

KW - RSK correspondence

KW - Transpositions

UR - http://www.scopus.com/inward/record.url?scp=80052037537&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2011.08.003

DO - 10.1016/j.jcta.2011.08.003

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AN - SCOPUS:80052037537

SN - 0097-3165

VL - 119

SP - 63

EP - 82

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 1

ER -