论文标题
识别自轭分区
Identifying Self-Conjugate Partitions
论文作者
论文摘要
正整数$ n $的分区定义为非插入序列$ p = [y__0，y_1，...，...，y_m] $的正整数$，总和为$ n $，其中$ y_i $称为分区的$ parts $。年轻的图是使用一行框的分区的视觉表示，其中每一行盒子对应于零件。共轭分区类似于矩阵的转置；我们用列或零件本身的零件索引切换行。自轭分区是等于它们的共轭的分区。以前，验证分区是否是自轭的唯一已知方法是通过使用年轻图。在这项研究中，通过证明初步的引理和定理有关易于识别形状的对称形状的定理，我们就会取得主要结果：简单地添加适当的零件的多样性，我们可以在没有年轻图的情况下表明分区是否是自偶联的。
A partition of a positive integer $n$ is defined as a non-increasing sequence $P = [y_0, y_1, ..., y_m]$ of positive integers which sum to $n$, where the $y_i$ are called the $parts$ of the partition. A Young diagram is a visual representation of a partition using rows of boxes, where each row of boxes corresponds to a part. The conjugate partition is similar to a transpose of a matrix; we switch the rows with columns, or the index of a part with the part itself. Self-conjugate partitions are partitions that are equal to their conjugate; previously, the only known way to verify whether a partition is self-conjugate was through the use of a Young diagram. In this research, by proving preliminary lemmas and theorems about easily identifiable shapes which are symmetric, we come to the main result: by simply adding the multiplicities of parts appropriately, we can show whether or not a partition is self-conjugate without the use of a Young diagram.
