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arXiv · 2311.03155

Comparison of symbolic and ordinary powers of parity binomial edge ideals

Nadia Taghipour·Shamila Bayati·Farhad Rahmati
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Abstract

In this paper, we investigate when symbolic and ordinary powers of the parity binomial edge ideal of a graph fail to be equal. It turns out that if $\mathcal{I}_{G}$ is the parity binomial edge ideal of a graph $G$, then in each of the following cases the symbolic power $\mathcal{I}_{G}^{(t)}$ and the ordinary power $\mathcal{I}_{G}^t$ are not equal for some $t$: (i) the clique number of $G$ is greater than 3; (ii) $G$ has a net; or (iii) $G$ has a PT as an induced subgraph.

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Nadia Taghipour, Shamila Bayati, Farhad Rahmati. 2023-11-06. Comparison of symbolic and ordinary powers of parity binomial edge ideals. https://doi.org/10.1007/s00605-023-01912-4

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