论文标题
标准和严格年轻图的归一化维度的渐近行为 - 生长和振荡
Asymptotic behaviour of normalized dimensions of standard and strict Young diagrams -- growth and oscillations
论文作者
论文摘要
在本文中，我们介绍了计算机研究的渐近学调查结果，以实现对称组的线性和投影表示的最大程度。这个问题减少了对最大维度标准和严格的年轻图的研究。我们为具有极大维度的标准和严格的年轻图构建了一些序列。 30年前，提出了归一化维度的限制的猜想[A.〜M。〜Vershik和S.〜V。〜Kerov，1985]，尚未得到证明。我们研究了年轻图序列中归一化尺寸函数的生长和振荡。我们的方法基于分析其标准化维度的有限差异。该分析还使我们可以对极限常数进行更精确的估计。
In this paper, we present the results of a computer investigation of asymptotics for maximum dimensions of linear and projective representations of the symmetric group. This problem reduces to the investigation of standard and strict Young diagrams of maximum dimensions. We constructed some sequences for both standard and strict Young diagrams with extremely large dimensions. The conjecture that the limit of normalized dimensions exists was proposed 30 years ago [A.~M.~Vershik and S.~V.~Kerov, 1985] and has not been proved yet. We studied the growth and oscillations of the normalized dimension function in sequences of Young diagrams. Our approach is based on analyzing finite differences of their normalized dimensions. This analysis also allows us to give much more precise estimation of the limit constants.
