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
The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux repre...The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux representations. This in turn is found to be an aspect of multipartite partitions. We discover, and show, that partitions can be expressed algebraically and can be “differentiated” and “integrated”. We show a complete set of bipartite and tripartite partitions, indicating equivalences for the root-pattern problem, for select pairs and triples. Tables enumerating the number of bipartite and tripartite partitions, for small pairs and triples are given in an appendix.展开更多
In this paper, the sematics of a paraconsistent logic and its nonmonotonic extension by minimal inconsistency are presented first. And then signed tableaux for paraconsistelit logic and minimal tableaux for logic of...In this paper, the sematics of a paraconsistent logic and its nonmonotonic extension by minimal inconsistency are presented first. And then signed tableaux for paraconsistelit logic and minimal tableaux for logic of minimal inconsistency is proposetl. Finally the reduction of logic of paraconsistency and minimal inconsistency on ordinary semantics which provides new approach to proof procedure and implementation of paraconsistency and minimal inconsistency are provided.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
Let π be a minimal ErdSs-Szekeres permutation of 1, 2,..., n^2, and let ln,k be the length of the longest increasing subsequence in the segment （πr（1）,...,π（k））. Under uniform measure we establish an exponent...Let π be a minimal ErdSs-Szekeres permutation of 1, 2,..., n^2, and let ln,k be the length of the longest increasing subsequence in the segment （πr（1）,...,π（k））. Under uniform measure we establish an exponentially decaying bound of the upper tail probability for ln,k, and as a consequence we obtain a complete convergence, which is an improvement of Romik＇s recent result. We also give a precise lower exponential tail for ln,k.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.
文摘The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux representations. This in turn is found to be an aspect of multipartite partitions. We discover, and show, that partitions can be expressed algebraically and can be “differentiated” and “integrated”. We show a complete set of bipartite and tripartite partitions, indicating equivalences for the root-pattern problem, for select pairs and triples. Tables enumerating the number of bipartite and tripartite partitions, for small pairs and triples are given in an appendix.
文摘In this paper, the sematics of a paraconsistent logic and its nonmonotonic extension by minimal inconsistency are presented first. And then signed tableaux for paraconsistelit logic and minimal tableaux for logic of minimal inconsistency is proposetl. Finally the reduction of logic of paraconsistency and minimal inconsistency on ordinary semantics which provides new approach to proof procedure and implementation of paraconsistency and minimal inconsistency are provided.
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.
基金Supported by National Natural Science Foundation of China （Grant No. 10671176） and Natural Science Foun- dation of Zhejiang Province （Grant No. J20091364）
文摘Let π be a minimal ErdSs-Szekeres permutation of 1, 2,..., n^2, and let ln,k be the length of the longest increasing subsequence in the segment （πr（1）,...,π（k））. Under uniform measure we establish an exponentially decaying bound of the upper tail probability for ln,k, and as a consequence we obtain a complete convergence, which is an improvement of Romik＇s recent result. We also give a precise lower exponential tail for ln,k.
