Journal of Integer Sequences, Vol. 21 (2018), Article 18.5.3

Jeu de Taquin of Set-Valued Young Tableaux

Paul Drube and Nichole Smith
Department of Mathematics and Statistics
Valparaiso University
Valparaiso, IN 46383


Jeu de taquin is a well-known operation on standard Young tableaux that may be used to define an equivalence relation on tableaux of any fixed rectangular shape. Via the well-studied bijection between two-row standard Young tableaux and non-crossing matchings, jeu de taquin is known to correspond to rotation of the associated matching by one strand. In this paper, we adapt jeu de taquin to standard set-valued Young tableaux a generalization of standard Young tableaux where cells contain unordered sets of integers. Our modified jeu de taquin operation is shown to correspond to to rotation of various classes of non-crossing matchings by one strand. In the case corresponding to k-equal non-crossing matchings, closed formulas are derived for the number of jeu de taquin equivalence classes of standard set-valued Young tableaux.

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(Concerned with sequences A002995 A054362 A054365 A054368 A054423.)

Received October 23 2017; revised versions received May 23 2018; May 24 2018. Published in Journal of Integer Sequences, May 25 2018.

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