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

Christian Krattenthaler

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

Combinatorics 2016-08-29 v3

Authors: Christian Krattenthaler

Abstract

We prove that the number of oscillating tableaux of length $n$ with at most $k$ columns, starting at $\emptyset$ 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

oscillating tableaux standard Young tableaux growth diagrams bijections semistandard tableaux

Cite

@article{arxiv.1412.5646,
  title  = {Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams},
  author = {Christian Krattenthaler},
  journal= {arXiv preprint arXiv:1412.5646},
  year   = {2016}
}

Comments

AmS-TeX; 16 pages; added a discussion section. arXiv admin note: text overlap with arXiv:math/0510676

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

Abstract

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