两类空心阶梯型标准杨表的计数  

Enumeration of Two Hollow Shapes of Shifted Standard Young Tableaux

作　　者：李秋营 白建侠 LI Qiuying;BAI Jianxia(Department of Mathematics,Tianjin Renai College,Tianjin 301636,China)

机构地区：[1]天津仁爱学院数学教学部,天津301636

出　　处：《云南师范大学学报（自然科学版）》2023年第5期29-35,共7页Journal of Yunnan Normal University:Natural Sciences Edition

基　　金：国家自然科学基金资助项目(12202309);天津市教委科研计划资助项目(2022KJ049).

摘　　要：通过嵌套顺序统计量与标准杨表之间的对应关系,将标准杨表的计数问题转化成相应嵌套顺序统计量上的多重积分问题,结合组合恒等式给出了近似直角梯形的空心阶梯型标准杨表的一般求和表示,并证明了一个关于平移阶梯型标准杨表数量的猜想.The correspondence between nested ordinal statistics and standard poplar tables is established,and the counting problem of standard Young tableaux is transformed into a multiple integral problem on the corresponding nested ordinal statistics.Otherwise,we combine with the combinatorial identity,the general summation representation of hollow shifted standard Young tableaux with approximately right-angled trapezoids is given,and a conjecture about the number of hollow shifted standard Young tableaux is proved in the literature.

关 键 词：标准杨表 空心阶梯型 多重积分 CATALAN数 

分 类 号：O157[理学—数学]