What question did this study set out to answer?

This research aims to derive exact formulas for the depth of the quotient ring related to edge ideals of increasing weighted paths.

Depth of powers of the edge ideal of an increasing weighted path

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This research aims to derive exact formulas for the depth of the quotient ring related to edge ideals of increasing weighted paths.
Developed mathematical formulas specific to powers of edge ideals.
Analyzed properties of quotient rings in the context of algebraic geometry.
Exact formulas for the depth of the quotient ring are established.
The findings enhance the understanding of edge ideals in increasing weighted paths.

We provide formulas for the depth of the quotient ring of powers of the edge ideal in weighted paths, suggesting new mathematical insights.

We provide exact formulas for the depth of the quotient ring of powers of the edge ideal of an increasing weighted path.

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Li et al. (2026) studied this question.

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We provide formulas for the depth of the quotient ring of powers of the edge ideal in weighted paths, suggesting new mathematical insights.

We provide exact formulas for the depth of the quotient ring of powers of the edge ideal of an increasing weighted path.