论文标题
依次一致的分区的双线，概括和其他特性
Bijections, generalizations, and other properties of sequentially congruent partitions
论文作者
论文摘要
最近，施耐德（Schneider）和施耐德（Schneider）定义了一个新的分区，称为顺序一致的分区，其中每个部分都与下一个部分Modulo的索引一致，他们证明了涉及这些分区的两种分区射击。我们介绍了特定于依次一致的分区的新分区符号，这使我们能够更容易地研究这些肉类及其组成，并根据年轻的图转换来重新解释它们。我们还定义了依次一致的分区的概括，并为这些概括性的一致分区提供了几种新的分区射击。最后，我们研究了施耐德（Schneider）的问题 - 施耐德（Schneider），涉及对安德鲁斯（Andrews）的分区理想理论的顺序一致分区。我们证明，依次一致的分区的最大分区理想具有无限顺序，因此没有链接，并且我们确定了其1个下层阶。
Recently, Schneider and Schneider defined a new class of partitions called sequentially congruent partitions, in which each part is congruent to the next part modulo its index, and they proved two partition bijections involving these partitions. We introduce a new partition notation specific to sequentially congruent partitions which allows us to more easily study these bijections and their compositions, and we reinterpret them in terms of Young diagram transformations. We also define a generalization of sequentially congruent partitions, and we provide several new partition bijections for these generalized sequentially congruent partitions. Finally, we investigate a question of Schneider--Schneider regarding how sequentially congruent partitions fit into Andrews' theory of partition ideals. We prove that the maximal partition ideal of sequentially congruent partitions has infinite order and is therefore not linked, and we identify its order 1 subideals.
