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Enumeration of row-increasing tableaux of two-row skew shapes
Discrete Mathematics ( IF 0.8 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.disc.2020.112254
Xiaomei Chen

Abstract In this paper, we firstly extend a result of Bonin, Shapiro and Simion by giving the distribution of the major index over generalized Schroder paths. Then by providing a bijection between generalized Schroder paths and row-increasing tableaux of skew shapes with two rows, we obtain the distribution of the major index and the amajor index over these tableaux, which extends a result of Du, Fan and Zhao. We also generalize a result of Pechenik and give the distribution of the major index over increasing tableaux of skew shapes with two rows. Especially, a bijection from row-increasing tableaux with shape ( n , m ) and maximal value n + m − k to standard Young tableaux with shape ( ( n − k + 1 , m − k + 1 , 1 k ) ∕ ( 1 2 ) ) is obtained.

中文翻译:

两行倾斜形状的行增加表的枚举

摘要 在本文中,我们首先通过给出主指数在广义施罗德路径上的分布来扩展Bonin、Shapiro 和Simion 的结果。然后通过提供广义施罗德路径和两行倾斜形状的行增加表之间的双射,我们得到主索引和主索引在这些表上的分布,扩展了杜、范和赵的结果。我们还概括了 Pechenik 的结果,并给出了主要指数在两行倾斜形状的增加表上的分布。特别是,从具有形状 ( n , m ) 和最大值 n + m − k 的行增加表到具有形状 ( ( n − k + 1 , m − k + 1 , 1 k ) ∕ ( 1 2 ) ) 得到。
更新日期:2021-03-01
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