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October 3, 2025Open Access

Associated primes of powers of edge ideals of edge-weighted trees

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The complete description of associated primes reveals complex relationships within edge ideals of trees.
Powers of edge ideals show distinct characteristics related to the structure of increasing weighted trees.
Analyzing associated primes contributes to understanding algebraic properties in edge-weighted structures.
This study emphasizes the importance of edge ideals in algebraic geometry, particularly in tree configurations.

This analysis details associated primes of edge ideals in edge-weighted trees, suggesting significant findings for polynomial relationships.

In this paper, we give a complete description of the associated primes of each power of the edge ideal of an increasing weighted tree.

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Li et al. (2025) studied this question.

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This analysis details associated primes of edge ideals in edge-weighted trees, suggesting significant findings for polynomial relationships.

In this paper, we give a complete description of the associated primes of each power of the edge ideal of an increasing weighted tree.