论文标题
分区图中的对数正态分布
Lognormal Degree Distribution in the Partition Graphs
论文作者
论文摘要
我们演示了一种将N的所有普通分区列为长度（N-1）的方法。充满锤子距离的由此产生的家族产生了锤子图的子图。对于普通分区的2灰色代码的存在遵循以下事实：图（省略了所有0个分区）是2相关的。但是，当n> 7时，这些图形不可能成为普通分区的哈密顿量，排除了所有此类翻转图的灰色代码的可能性。我们进一步研究了n的图的度分布，并提供了计算证据，表明这是一个长尾的对数正态分布。该猜想与分区零件数量分布的紧密相关且较旧的问题联系在一起，相同的证据表明，对于大n，该分布也是对数正态的。这些方法扩展到n的较高维分区，然后可以写为d + 1个字母上的长度（n-1）单词。所得图是连接的，证明了D维分区允许使用3灰色代码。
We demonstrate a method for listing all ordinary partitions of n as binary words of length (n-1). The resulting family imbued with the hamming distance yields subgraphs of the Hamming Graphs. The existence of a 2-Gray Code for ordinary partitions follows from the fact that the graph (with the all 0s partition omitted) is 2-connected. However, the graphs fail to be hamiltonian for ordinary partitions when n > 7, ruling out the possibility of a Gray code for all such flip graphs. We further investigate the degree distribution of the graph for n, and provide computational evidence that this is a long-tailed lognormal distribution. This conjecture connects to a closely related, and much older, question of the distribution of the number of parts of a partition and the same evidence suggests that this distribution is also lognormal for large n. These methods extend to higher dimensional partitions of n which can be then written as words of length (n-1) on d + 1 letters. The resulting graphs are connected, proving that d-dimensional partitions allow a 3-Gray code.
