共查询到20条相似文献,搜索用时 0 毫秒
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Steven Pon 《Journal of Algebraic Combinatorics》2012,36(4):595-622
We introduce affine Stanley symmetric functions for the special orthogonal groups, a class of symmetric functions that model the cohomology of the affine Grassmannian, continuing the work of Lam and Lam, Schilling, and Shimozono on the special linear and symplectic groups, respectively. For the odd orthogonal groups, a Hopf-algebra isomorphism is given, identifying (co)homology Schubert classes with symmetric functions. For the even orthogonal groups, we conjecture an approximate model of (co)homology via symmetric functions. In the process, we develop type B and type D non-commutative k-Schur functions as elements of the affine nilCoxeter algebra that model homology of the affine Grassmannian. Additionally, Pieri rules for multiplication by special Schubert classes in homology are given in both cases. Finally, we present a type-free interpretation of Pieri factors, used in the definition of noncommutative k-Schur functions or affine Stanley symmetric functions for any classical type. 相似文献
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A two functions symmetric nonlinear minimax theorem 总被引:2,自引:0,他引:2
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We construct a generic extension in which the ℵ2nd canonical function on ℵ1 exists.
Supported by NSF and by a Fulbright grant.
Publ. 378. Partially supported by the B.S.F. 相似文献
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Ernst-Ulrich Gekeler 《Journal of Number Theory》1985,21(2):135-140
A formula expressing the Drinfeld discriminant as a product of cyclotomic polynomials is proved. 相似文献
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本文用一种新方法研究两类对称函数的Schur凸性.首先,对x=(x1,...,xn)∈(-∞,1)n∪(1,+∞)n和r∈{1,2,...,n},讨论Guan(2007)定义的对称函数Fn(x,r)=Fn(x1,x2,...,xn;r)=∑1≤i1≤i2≤···≤ir≤n r∏j=1xij/(1-xij)的Schur凸性,其中i1,i2,...,in为正整数;推广褚玉明等人(2009)的主要结果,因而用新方法推广并解决Guan(2007)提出的一个公开问题.然后,对x=(x1,...,xn)∈(-∞,1)n∪(1,+∞)n和r∈{1,2,...,n},研究本文定义的对称函数Gn(x,r)=Gn(x1,x2,...,xn;r)=∑1≤i1≤i2≤···≤ir≤n(r∏j=1xij/(1-xij))1/r的Schur凸性、Schur乘性凸性和Schur调和凸性,其中i1,i2,...,in为正整数.作为应用,用Schur凸函数自变量的双射变换得到其他几类对称函数的Schur凸性,用控制理论建立一些不等式,特别地,由此给出Sharpiro不等式和Ky Fan不等式一个共同的推广,导出Safta猜想在高维空间的推广. 相似文献
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J. Behboodian 《Journal of Theoretical Probability》1989,2(2):267-270
The symmetry of the sum and product of two independent random variablesX andY, whenX orY is not symmetric, is studied. 相似文献
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We prove that for any infinite , the full symmetric group is the product of at most abelian subgroups. This is a strengthening of a recent result of M. Abért.
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Mathematical Programming - We investigate in this paper the generalized trust region subproblem (GTRS) of minimizing a general quadratic objective function subject to a general quadratic inequality... 相似文献
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Let xi ≥ 0, yi ≥ 0 for i = 1,…, n; and let aj(x) be the elementary symmetric function of n variables given by aj(x) = ∑1 ≤ ii < … <ij ≤ nxii … xij. Define the partical ordering x <y if aj(x) ≤ aj(y), j = 1,… n. We show that , where {xα}i = xαi. We also give a necessary and sufficient condition on a function f(t) such that x <y ? f(x) <f(y). Both results depend crucially on the following: If x <y there exists a piecewise differentiable path z(t), with zi(t) ≥ 0, such that z(0) = x, z(1) = y, and z(s) <z(t) if 0 ≤ s ≤ t ≤ 1. 相似文献
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We establish a combinatorial interpretation for various operations on symmetric functions, such as plethysm, scalar product, and derivation. Thus we obtain proofs of formulas involving symmetric functions in term of combinatorial constructions on permutations. 相似文献
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Nguyen Xuan Hong 《Comptes Rendus Mathematique》2018,356(8):865-869
In this note, we give a characterization for the weighted log canonical thresholds of plurisubharmonic functions. As an application, we prove an inequality for weighted log canonical thresholds and Monge–Ampère masses. 相似文献