多项式序列的广义Turán表达式的Hurwitz稳定性
Hurwitz Stability of Generalized Turán Expressions of Polynomial Sequences
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中文总结 AI 辅助
本文证明了Eulerian和Narayana多项式的Turán表达式稳定性猜想，推广了Turán表达式概念，给出广义稳定性判定准则，并应用于递推多项式序列。
中文摘要 AI 辅助
本文证明了Eulerian多项式的强Turán表达式的弱Hurwitz稳定性猜想，以及Liu和Yan提出的关于Narayana多项式的相应猜想。我们推广了多项式序列的Turán表达式的概念，并为广义Turán表达式的广义稳定性提供了一个判定准则。基于我们的充分条件，我们不仅证实了Liu和Yan的猜想，还获得了某类递推多项式序列和广义Narayana多项式的广义Turán表达式的广义稳定性。
英文摘要
In this paper we prove the weak Hurwitz stability conjecture for the strong Turán expressions of Eulerian polynomials, as well as the corresponding conjecture for Narayana polynomials, which were conjectured by Liu and Yan. We generalize the notion of Turán expressions of polynomial sequences, and provide a criterion for the generalized stability of generalized Turán expressions. Based on our sufficient condition, we not only confirm Liu and Yan's conjectures but also obtain the generalized stability of generalized Turán expressions of a class of recurrent polynomial sequences and generalized Narayana polynomials.
发表机构
- Center for Combinatorics, LPMC Nankai University（南开大学组合数学中心，LPMC）
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