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arXiv · 2312.02687

On the Equality of Symbolic and Ordinary Powers of Binomial Edge Ideals

Iman Jahani·Shamila Bayati·Farhad Rahmati
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Abstract

In this paper, we investigate whether the symbolic and ordinary powers of a binomial edge ideal $J_{G}$ are equal. We show that the equality $J_{G}^{t}=J_{G}^{(t)}$ holds for every $t \geq 1$ when $|Ass(J_{G})|=2$. Moreover, if $G$ is a caterpillar tree, then one has the same equality. Finally, we characterize the generalized caterpillar graphs which the equality of symbolic and ordinary powers of $J_{G}$ occurs.

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Iman Jahani, Shamila Bayati, Farhad Rahmati. 2023-12-05. On the Equality of Symbolic and Ordinary Powers of Binomial Edge Ideals. https://doi.org/10.1007/s00574-022-00323-7

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