Abstract
Let S = K[x1; x2;...; xn] be the polynomial ring in n variables over a field K; and let I be a squarefree monomial ideal minimally generated by the monomials u1; u2;...; um: Let w be the smallest number t with the property that for all integers 1 6 i1 < i2 <... < i t 6 m such that \(lcm({u_{{i_1}}},{u_{{i_2}}},...,{u_{{i_t}}}) = lcm({u_1},{u_2},...,{u_m})\) We give an upper bound for Castelnuovo-Mumford regularity of I by the bigsize of I: As a corollary, the projective dimension of I is bounded by the number w.
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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Grant No. 11201326), the Natural Science Foundation of Jiangsu Province (No. BK2011276), and the Jiangsu Provincial Training Programs of Innovation and Entrepreneurship for Undergraduates.
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Chu, L., Liu, S. & Tang, Z. Castelnuovo-Mumford regularity and projective dimension of a squarefree monomial ideal. Front. Math. China 13, 277–286 (2018). https://doi.org/10.1007/s11464-017-0680-x
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DOI: https://doi.org/10.1007/s11464-017-0680-x