对称矩阵热带特征多项式的性质
Properties of the Tropical Characteristic Polynomial of Symmetric Matrices
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中文总结 AI 辅助
研究对称矩阵热带特征多项式的组合结构，利用主子矩阵的热带积，建立首项系数新不等式，揭示系数序列凹性及必要条件，加深对其结构的理解。
中文摘要 AI 辅助
我们利用对称矩阵主子矩阵的热带积研究其热带特征多项式的组合结构。建立了热带特征多项式首项系数的新不等式，揭示了系数序列的凹性，并给出了一个序列作为对称矩阵热带特征多项式系数序列出现的必要条件。这些结果加深了对与对称矩阵相关的热带特征多项式结构的理解。
英文摘要
We investigate the combinatorial structure of the tropical characteristic polynomial of symmetric matrices using the tropical permanents of their principal submatrices. We establish new inequalities for the leading coefficients of the tropical characteristic polynomial, revealing concavity properties of the coefficient sequence and yielding necessary conditions for a sequence to arise as the coefficient sequence of the tropical characteristic polynomial of a symmetric matrix. These results provide a deeper understanding of the structure of tropical characteristic polynomials associated with symmetric matrices.
