论文标题
对称组的正常cayley图的Aldous'光谱间隙特性
Aldous' spectral gap property for normal Cayley graphs on symmetric groups
论文作者
论文摘要
Aldous'光谱差距猜想指出，SN的标准表示可以实现对称组SN上任何连接的Cayley图的第二大特征值。这一著名的猜想在2010年以一般形式证明，激发了人们对在SN上寻找其他特征的Cayley图形家庭的兴趣。在本文中，我们证明了具有足够大的N具有该特性的正常Cayley图的三个结果，其中一个可以看作是Aldous'Spectral Gap uspointure的“正常”情况的概括。
Aldous' spectral gap conjecture states that the second largest eigenvalue of any connected Cayley graph on the symmetric group Sn with respect to a set of transpositions is achieved by the standard representation of Sn. This celebrated conjecture, which was proved in its general form in 2010, has inspired much interest in searching for other families of Cayley graphs on Sn with the property that the largest eigenvalue strictly smaller than the degree is attained by the standard representation of Sn. In this paper, we prove three results on normal Cayley graphs on Sn possessing this property for sufficiently large n, one of which can be viewed as a generalization of the "normal" case of Aldous' spectral gap conjecture.
