We introduce tableau stabilization, a new phenomenon and statistic on Young tableaux based on jeu de taquin. We investigate bounds for tableau stabilization, the shape of stabilized tableaux, and tableau stabilization as a permutation statistic. We apply tableau stabilization to construct the sufficiently large rectangular tableaux fixed by powers of promotion, which were counted by Brendon Rhoades via the cyclic sieving phenomenon [(Rhoades in J Combin Theory Ser A 117(1):38–76, 2010), Theorem 1.3].

中文翻译：

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提升力固定的Tableau稳定度和矩形Tableaux

介绍了基于jeu de taquin的Young tableaux的画面稳定，一种新现象和统计数据。我们调查画面稳定，边界稳定的形状和画面稳定作为置换统计量的范围。我们应用场景稳定来构造由提升力固定的足够大的矩形场景，布伦登·罗德斯通过循环筛分现象对其进行了计数[（Rhoades in J Combin Theory Ser A 117（1）：38-76，2010），定理1.3]。