新的基于判别式的乘子序列
New Multiplier Sequences via Discriminant Amoebae
摘要：
在他们1914年的经典论文中，Polya和Schur引入并刻画了两种类型的对角作用于R[x]的单项式基的线性算子，发送实根多项式（分别为：所有非零根都具有相同符号的多项式）到实根多项式。受Gelfand，Kapranov和Zelevinsky发现的变形虫和判别式的基本性质的启发，我们引入了两个新的自然类多项式，并描述了保留这些新类的对角算子。在我们的描述中，一个令人愉快的情况是，这些类有一个简单的明确的描述，其中之一与对数凹序列的类相吻合。
英文摘要：
In their classic 1914 paper, Polya and Schur introduced and characterized two types of linear operators acting diagonally on the monomial basis of R[x], sending real-rooted polynomials (resp. polynomials with all nonzero roots of the same sign) to real-rooted polynomials. Motivated by fundamental properties of amoebae and discriminants discovered by Gelfand, Kapranov, and Zelevinsky, we introduce two new natural classes of polynomials and describe diagonal operators preserving these new classes. A pleasant circumstance in our description is that these classes have a simple explicit description, one of them coinciding with the class of log-concave sequences.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
