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تسجيل مستخدم جديدComparision between regularity of small symbolic powers and ordinary powers of an edge ideal
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Let $G$ be a simple graph and $I$ its edge ideal. We prove that $${rm reg}(I^{(s)}) = {rm reg}(I^s)$$ for $s = 2,3$, where $I^{(s)}$ is the $s$-th symbolic power of $I$. As a consequence, we prove the following bounds begin{align*} {rm reg} I^{s} & le {rm reg} I + 2s - 2, text{ for } s = 2,3, {rm reg} I^{(s)} & le {rm reg} I + 2s - 2,text{ for } s = 2,3,4. end{align*}
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