共查询到11条相似文献,搜索用时 0 毫秒
1.
William Y. C. Chen Guo-Guang Yan Arthur L. B. Yang 《European Journal of Combinatorics》2004,25(8):1181
We obtain a tableau definition of the skew Schubert polynomials named by Lascoux, which are defined as flagged double skew Schur functions. These polynomials are in fact Schubert polynomials in two sets of variables indexed by 321-avoiding permutations. From the divided difference definition of the skew Schubert polynomials, we construct a lattice path interpretation based on the Chen–Li–Louck pairing lemma. The lattice path explanation immediately leads to the determinantal definition and the tableau definition of the skew Schubert polynomials. For the case of a single variable set, the skew Schubert polynomials reduce to flagged skew Schur functions as studied by Wachs and by Billey, Jockusch, and Stanley. We also present a lattice path interpretation for the isobaric divided difference operators, and derive an expression of the flagged Schur function in terms of isobaric operators acting on a monomial. Moreover, we find lattice path interpretations for the Giambelli identity and the Lascoux–Pragacz identity for super-Schur functions. For the super-Lascoux–Pragacz identity, the lattice path construction is related to the code of the partition which determines the directions of the lines parallel to the y-axis in the lattice. 相似文献
2.
Skew Hadamard difference sets have been an interesting topic of study for over 70 years. For a long time, it had been conjectured the classical Paley difference sets (the set of nonzero quadratic residues in where ) were the only example in Abelian groups. In 2006, the first author and Yuan disproved this conjecture by showing that the image set of is a new skew Hadamard difference set in with m odd, where denotes the first kind of Dickson polynomials of order n and . The key observation in the proof is that is a planar function from to for m odd. Since then a few families of new skew Hadamard difference sets have been discovered. In this paper, we prove that for all , the set is a skew Hadamard difference set in , where m is odd and . The proof is more complicated and different than that of Ding‐Yuan skew Hadamard difference sets since is not planar in . Furthermore, we show that such skew Hadamard difference sets are inequivalent to all existing ones for by comparing the triple intersection numbers. 相似文献
3.
最近,孙华定义了一类新的精细化Eulerian多项式,即$$A_n(p,q)=\sum_{\pi\in \mathfrak{S}_n}p^{{\rm odes}(\pi)}q^{{\rm edes}(\pi)},\ \ n\ge 1,$$ 其中$S_n$表示$\{1,2,\ldots,n\}$上全体$n$阶排列的集合, odes$(\pi)$与edes$(\pi)$分别表示$S_n$中排列$\pi$的奇数位与偶数位上降位数的个数.本文利用经典的Eulerian多项式$A_n(q)$ 与Catalan 序列的生成函数$C(q)$,得到精细化Eulerian 多项式$A_n(p,q)$的指数型生成函数及$A_n(p,q)$的显示表达式.在一些特殊情形,本文建立了$A_n(p,q)$与$A_n(0,q)$或$A_n(p,0)$之间的联系,并利用Eulerian数表示多项式$A_n(0,q)$的系数.特别地,这些联系揭示了Euler数$E_n$与Eulerian数$A_{n,k}$之间的一种新的关系. 相似文献
4.
Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes
Ronald C. King Trevor A. Welsh Stephanie J. van Willigenburg 《Journal of Algebraic Combinatorics》2008,28(1):139-167
Some new relations on skew Schur function differences are established both combinatorially using Schützenberger’s jeu de taquin,
and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew
Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions
confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences
of products of Schubert classes are Schubert positive.
For Manfred Schocker 1970–2006.
S.J. van Willigenburg was supported in part by the National Sciences and Engineering Research Council of Canada. 相似文献
5.
Yu. A. Neretin 《Functional Analysis and Its Applications》2005,39(2):106-119
We obtain the spectral decomposition of the hypergeometric differential operator on the contour Re z = 1/2. (The multiplicity of the spectrum of this operator is 2.) As a result, we obtain a new integral transform different from the Jacobi (or Olevskii) transform. We also construct an 3
F
2-orthogonal basis in a space of functions ranging in ℂ2. The basis lies in the analytic continuation of continuous dual Hahn polynomials with respect to the index n of a polynomial.__________Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 31–46, 2005Original Russian Text Copyright © by Yu. A. Neretin 相似文献
6.
本文证明了Morgan-Voyce多项式的零点在闭区间$[-4,0]$上是稠密的.本文也证明了Morgan-Voyce多项式系数的分布是渐近正态的,以及它的系数矩阵是全正的. 相似文献
7.
设Bm(f,·)为函数f在d维单纯形σ上的n阶Bernstein多项式,本文对f∈Cr(σ)及f∈Cr+2(σ)给出了f的各阶编导数用Bn(f,·)相应偏导数逼近的误差估计.同时也考虑了整系数Bernstein多项式的Lp模估计 相似文献
8.
S. P. Sidorov 《Journal of Approximation Theory》2002,118(2):188-201
In this paper, we will show that Lagrange interpolatory polynomials are optimal for solving some approximation theory problems concerning the finding of linear widths.In particular, we will show that
, where
n is a set of the linear operators with finite rank n+1 defined on
−1,1], and where
n+1 denotes the set of polynomials p=∑i=0n+1aixi of degreen+1 such that an+11. The infimum is achieved for Lagrange interpolatory polynomial for nodes
. 相似文献
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10.
Dan Miclu 《Mathematical Methods in the Applied Sciences》2019,42(16):5317-5330
In this article, we try to assign a place on the map of the closed Newton–Cotés quadrature formulas to a new approximation formula based on the classical Bernstein polynomials. We create a procedure for a computer implementation that allows us to verify the accuracy of the new approximation formula. In order to get a complete image of this kind of approximation, we compare some well‐known quadrature formulas. Although effective in most situations, there are instances when the composite quadrature formulas cannot be applied, as they use equally‐spaced nodes. We present also an adaptive method that is used to obtain better approximations and to minimize the number of function evaluations. Numerical examples are given to increase the validity of the theoretical aspects. 相似文献