论文标题
关于分区数量
On the Schaper Number of Partitions
论文作者
论文摘要
计算对称组的分解数的最有用的工具之一是Schaper的总和公式。可以通过了解相应分区的chaper编号来改进此公式对给定SPECHT模块的效用。 Fayers给出了这些分区至少两个分区的表征。在本文中，我们将证明如何使用此知识来计算一些分解数，然后再扩展该结果，希望将来可以计算出更多的分解数。对于$ p = 2 $，我们将对校长编号至少三个的分区进行完整的表征，而那些至少四个的分区。我们还提供了一个必要条件的列表，以使分区的奇数至少三个奇数和对这些条件充分性的猜想。
One of the most useful tools for calculating the decomposition numbers of the symmetric group is Schaper's sum formula. The utility of this formula for a given Specht module can be improved by knowing the Schaper Number of the corresponding partition. Fayers gives a characterisation of those partitions whose Schaper number is at least two. In this paper we shall demonstrate how this knowledge can be used to calculate some decomposition numbers before extending this result with the hope of allowing more decomposition numbers to be calculated in the future. For $p=2$ we shall give a complete characterisation of partitions whose Schaper number is at least three, and those whose Schaper number at least four. We also present a list of necessary conditions for a partition to have Schaper number at least three for odd primes and a conjecture on the sufficiency of these conditions.
