顺序统计量在非参数统计分析中有着广泛的应用,嵌套顺序统计量的分布则依赖于具体的嵌套结构以及随机变量的分布特性.在研究三段式嵌套顺序统计量的分布时,可以将问题转化为嵌套积分,通过对相应的嵌套单形进行多重积分得到三段式嵌套顺...顺序统计量在非参数统计分析中有着广泛的应用,嵌套顺序统计量的分布则依赖于具体的嵌套结构以及随机变量的分布特性.在研究三段式嵌套顺序统计量的分布时,可以将问题转化为嵌套积分,通过对相应的嵌套单形进行多重积分得到三段式嵌套顺序统计量的分布.这种分析方法的应用十分广泛,由于Standard Young Tableaux (SYT)的每一行对应一组独立的顺序统计量,因此文章将其应用于SYT的计数问题.此外,文章还将三段式嵌套顺序统计量的分布应用于选票问题.展开更多
Let Uq(osp(1|2n)) be the quantized enveloping superalgebra corresponding to the Lie superalgebra osp(1|2n). In terms of semistandard Young tableaux satisfying some additional conditions, a realization of crystal graph...Let Uq(osp(1|2n)) be the quantized enveloping superalgebra corresponding to the Lie superalgebra osp(1|2n). In terms of semistandard Young tableaux satisfying some additional conditions, a realization of crystal graph of finite-dimensional irreducible modules of Uq(osp(1|2n)) is given. Also, the generalized LittlewoodRichardson rule for tensor product of crystal graphs is established.展开更多
Flagged skew tableaux are generalizationa of Young tableaux in which each row (column)has an upper and lower bound on the entries. It has been shown that they are enumerated byflagged skew Schur functions. By introduc...Flagged skew tableaux are generalizationa of Young tableaux in which each row (column)has an upper and lower bound on the entries. It has been shown that they are enumerated byflagged skew Schur functions. By introducing the dominance technique, we preeent an alternateproof for this conclusion directly.展开更多
文摘顺序统计量在非参数统计分析中有着广泛的应用,嵌套顺序统计量的分布则依赖于具体的嵌套结构以及随机变量的分布特性.在研究三段式嵌套顺序统计量的分布时,可以将问题转化为嵌套积分,通过对相应的嵌套单形进行多重积分得到三段式嵌套顺序统计量的分布.这种分析方法的应用十分广泛,由于Standard Young Tableaux (SYT)的每一行对应一组独立的顺序统计量,因此文章将其应用于SYT的计数问题.此外,文章还将三段式嵌套顺序统计量的分布应用于选票问题.
基金supported by National Natural Science Foundation of China (Grant Nos.10671016 10771014)Beijing Natural Science Foundation (Grant No. 1062003)
文摘Let Uq(osp(1|2n)) be the quantized enveloping superalgebra corresponding to the Lie superalgebra osp(1|2n). In terms of semistandard Young tableaux satisfying some additional conditions, a realization of crystal graph of finite-dimensional irreducible modules of Uq(osp(1|2n)) is given. Also, the generalized LittlewoodRichardson rule for tensor product of crystal graphs is established.
文摘Flagged skew tableaux are generalizationa of Young tableaux in which each row (column)has an upper and lower bound on the entries. It has been shown that they are enumerated byflagged skew Schur functions. By introducing the dominance technique, we preeent an alternateproof for this conclusion directly.
