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 -