P. A. MacMahon was the first to examine integer partitions in which consecutive integers were not allowed as parts. Such partitions may be described as having sequences of length 1. Recently it was shown that partitions containing no sequences of consecutive integers of length k are of interest in seemingly unrelated problems concerning threshold growth models. The object now is to develop the subject intrinsically to both provide deeper understanding of the theory and application of partitions and reveal the surprising role of Ramanujan's mock theta functions.
展开▼
机译：P. A. MacMahon是第一个研究不允许将连续整数作为部分的整数分区的人。可以将这样的分区描述为具有长度为1的序列。最近显示，在有关阈值增长模型的看似无关的问题中，不包含长度为k的连续整数的序列的分区是令人感兴趣的。现在的目的是从本质上发展该主题，以提供对分区理论和应用的更深刻理解，并揭示Ramanujan的模拟theta函数的惊人作用。
展开▼
