两类反阶梯中空型标准杨表计数

Two types of anti-step hollow standard Young tableaux counting

利用嵌套顺序统计量和标准杨表之间的一一对应关系,建立组合概率模型,用连续数学的思想去解决离散数学问题,研究了两类从东北角向西南角倾斜的反阶梯中空型标准杨表的计数问题。运用服从(0,1)均匀分布的嵌套顺序统计量的相关性质和嵌套多重积分、行列式积分等数学方法,得到了(n m+1\\σm)/((n-2)m\\σm-1)|{(1,2)}型和(n n+1\\σm)/((n-2)n\\σm-1)|{(1,2)}型两类标准杨表的计数公式。

Based on the one-to-one correspondence between nested order statistics and standard Young tableaux,this paper established a combined probability model to solve discrete mathematical problems with the idea of continuous mathematics,and studied the counting problem of two types of anti-step hollow standard Young tableaux inclined from northeast corner to southwest corner.By using the related properties of nested order statistics that obey the uniform distribution of(0,1)and mathematical methods such as nested multiple integrals and determinant integrals,we obtain two kinds of standard Young tables:(n m+1\\σm)/((n-2)m\\σm-1)|{(1,2)}and(n n+1\\σm)/((n-2)n\\σm-1)|{(1,2)}.