Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams

Christian Krattenthaler

doi:10.1016/j.jcta.2016.06.015

Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams

Christian Krattenthaler

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We prove that the number of oscillating tableaux of length n with at most k columns, starting at ∅ and ending at the one-column shape (1 ^m), is equal to the number of standard Young tableaux of size n with m columns of odd length, all columns of length at most 2k. This refines a conjecture of Burrill, which it thereby establishes. We prove as well a “Knuth-type” extension stating a similar equi-enumeration result between generalised oscillating tableaux and semistandard tableaux.

Original language	English
Pages (from-to)	277 - 291
Number of pages	15
Journal	Journal of Combinatorial Theory, Series A
Volume	144
DOIs	https://doi.org/10.1016/j.jcta.2016.06.015
Publication status	Published - Nov 2016

Austrian Fields of Science 2012

101012 Combinatorics

Keywords

ALGORITHM
FERRERS SHAPES
GRADED GRAPHS
Growth diagrams
KNUTH CORRESPONDENCES
Oscillating tableaux
ROBINSON-SCHENSTED CORRESPONDENCE
Robinson-Schensted correspondence
Robinson-Schensted-Knuth correspondence
Semistandard tableaux
Standard Young tableaux
YOUNG TABLEAUX
Robinson–Schensted correspondence
Robinson–Schensted–Knuth correspondence

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10.1016/j.jcta.2016.06.015

Cite this

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title = "Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams",

abstract = "We prove that the number of oscillating tableaux of length n with at most k columns, starting at ∅ and ending at the one-column shape (1 m), is equal to the number of standard Young tableaux of size n with m columns of odd length, all columns of length at most 2k. This refines a conjecture of Burrill, which it thereby establishes. We prove as well a “Knuth-type” extension stating a similar equi-enumeration result between generalised oscillating tableaux and semistandard tableaux. ",

keywords = "ALGORITHM, FERRERS SHAPES, GRADED GRAPHS, Growth diagrams, KNUTH CORRESPONDENCES, Oscillating tableaux, ROBINSON-SCHENSTED CORRESPONDENCE, Robinson-Schensted correspondence, Robinson-Schensted-Knuth correspondence, Semistandard tableaux, Standard Young tableaux, YOUNG TABLEAUX, Robinson–Schensted correspondence, Robinson–Schensted–Knuth correspondence",

author = "Christian Krattenthaler",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2016",

month = nov,

doi = "10.1016/j.jcta.2016.06.015",

language = "English",

volume = "144",

pages = "277 -- 291",

journal = "Journal of Combinatorial Theory, Series A",

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TY - JOUR

T1 - Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams

AU - Krattenthaler, Christian

PY - 2016/11

Y1 - 2016/11

N2 - We prove that the number of oscillating tableaux of length n with at most k columns, starting at ∅ and ending at the one-column shape (1 m), is equal to the number of standard Young tableaux of size n with m columns of odd length, all columns of length at most 2k. This refines a conjecture of Burrill, which it thereby establishes. We prove as well a “Knuth-type” extension stating a similar equi-enumeration result between generalised oscillating tableaux and semistandard tableaux.

AB - We prove that the number of oscillating tableaux of length n with at most k columns, starting at ∅ and ending at the one-column shape (1 m), is equal to the number of standard Young tableaux of size n with m columns of odd length, all columns of length at most 2k. This refines a conjecture of Burrill, which it thereby establishes. We prove as well a “Knuth-type” extension stating a similar equi-enumeration result between generalised oscillating tableaux and semistandard tableaux.

KW - ALGORITHM

KW - FERRERS SHAPES

KW - GRADED GRAPHS

KW - Growth diagrams

KW - KNUTH CORRESPONDENCES

KW - Oscillating tableaux

KW - ROBINSON-SCHENSTED CORRESPONDENCE

KW - Robinson-Schensted correspondence

KW - Robinson-Schensted-Knuth correspondence

KW - Semistandard tableaux

KW - Standard Young tableaux

KW - YOUNG TABLEAUX

KW - Robinson–Schensted correspondence

KW - Robinson–Schensted–Knuth correspondence

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U2 - 10.1016/j.jcta.2016.06.015

DO - 10.1016/j.jcta.2016.06.015

M3 - Article

SN - 0097-3165

VL - 144

SP - 277

EP - 291

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

ER -

Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams

Abstract

Austrian Fields of Science 2012

Keywords

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