Schur P-函数和Q-函数的Horn递归：扩展摘要

k-Schur函数的一个递推公式

A recursion formula for k-Schur functions

Bernstein算子允许递归地建立Schur函数。基于组合算子，推广了Bernstein算子，给出了k-Schur函数在t=1时的一个递推公式.递归立即导致的组合解释的展开系数的k-舒尔函数在t=1的齐次对称函数。

Macdonald 第7变体 Schur 多项式的 V/L 递归

The V/L recursion for Macdonald's 7th Variation Schur polynomials

本文推广并证明了 Macdonald 为其 Schur 函数“第7变体”猜想的一个递归关系，该变体是有限域上利用 Frobenius 幂模拟（直和斜）Schur 多项式的一族多项式。

Finding Planted Subgraphs with Few Eigenvalues using the Schur-Horn Relaxation

Extracting structured subgraphs inside large graphs - often known as the planted subgraph problem - is a fundamental question that arises in a range of application domains. This problem is NP-hard in general, and as a result, significant efforts have been directed towards the development of tractable procedures that succeed on specific families of problem instances. We propose a new computationally efficient convex relaxation for solving the planted subgraph problem; our approach is based on tractable semidefinite descriptions of majorization inequalities on the spectrum of a symmetric matrix.…

On Schur function expansions of Thom polynomials

We discuss computations of the Thom polynomials of singularity classes of maps in the basis of Schur functions. We survey the known results about the bound on the length and a rectangle containment for partitions appearing in such Schur function expansions. We describe several recursions for the coefficients. For some singularities, we give old and new computations of their Thom polynomials.

mod（p）与数域的k次线性递归

Degree-k linear recursions mod(p) and number fields

通过在整数向量$(t_1,...,t_k)$上计算广义斐波那契多项式序列$\{F_{k,n}(t_1,...,t_k)\}$（完全对称多项式的等压反射）来确定次数$k$的线性递归。如果$F_{k,n}(t_1,...,t_k) = f_n$，则$$f_n - \sum_{j=1}^k t_j f_{n-j} = 0,$$和$\{f_n\}$是次数为$k$的线性递归。一方面，这种序列模一个素数$p$的周期性质进行了讨论，并显示有关的素数结构的某些代数数域，例如，算术性能的周期示出的特征分歧素的扩张领域。另一方面，与数域相关联的半局部环的结构被证明完全由Schur-hook多项式决定。关键词：对称多项式，舒尔多项式，线性递归，数域。

Smooth entrywise positivity preservers, a Horn-Loewner master theorem, and symmetric function identities

A special case of a fundamental result of Loewner and Horn [Trans. Amer. Math. Soc. 1969] says that given an integer $n \geq 1$, if the entrywise application of a smooth function $f : (0,\infty) \to \mathbb{R}$ preserves the set of $n \times n$ positive semidefinite matrices with positive entries, then $f$ and its first $n-1$ derivatives are non-negative on $(0,\infty)$. In a recent joint work with Belton-Guillot-Putinar [J. Eur. Math. Soc., in press], we proved a stronger version, and used it to strengthen the Schoenberg-Rudin characterization of dimension-free positivity preservers [Duke Mat…