Abstract
In this paper, we explicitly give combinatorial formulas for the regularity of powers of edge ideals, \({\text {reg}}(I(D)^k)\), 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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Acknowledgements
Manohar Kumar is thankful to the Government of India for supporting him in this work through the Prime Minister Research Fellowship. The authors would like to thank the anonymous referee for careful reading of the manuscript and suggestions for improving the paper to the present version.
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Manohar Kumar: Supported by PMRF fellowship, India.
Ramakrishna Nanduri: Supported by SERB Grant No: CRG/2021/000465, India.
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Kumar, M., Nanduri, R. Regularity of powers of edge ideals of Cohen–Macaulay weighted oriented forests. J Algebr Comb 58, 867–893 (2023). https://doi.org/10.1007/s10801-023-01256-0
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DOI: https://doi.org/10.1007/s10801-023-01256-0