Regularity of powers of edge ideals of Cohen-Macaulay weighted oriented forests

Abstract

In this paper, we explicitly give combinatorial formulas for the regularity of powers of edge ideals, $\reg(I(D)^k)$, of weighted oriented unmixed forests $D$ whose leaves are sinks ($V^{+}(D)$ are sinks). This combinatorial formula is a piecewise linear function of $k$, for $k\ge 1$.

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