References
- A. Bagheri, M. Chardin, and H. T. Ha, The eventual shape of Betti tables of powers of ideals, Math. Res. Lett. 20 (2013), no. 6, 1033-1046. https://doi.org/10.4310/MRL.2013.v20.n6.a3
- A. Bagheri and K. Lamei, Graded Betti numbers of powers of ideals, J. Commut. Algebra 12 (2020), no. 2, 153-169. https://doi.org/10.1216/jca.2020.12.153
- A. Barvinok and J. E. Pommersheim, An algorithmic theory of lattice points in polyhedra, in New perspectives in algebraic combinatorics (Berkeley, CA, 1996-97), 91-147, Math. Sci. Res. Inst. Publ., 38, Cambridge Univ. Press, Cambridge, 1999.
- N. Bourbaki. Commutative Algebra, Addison Wesley, Reading, 1972.
- M. Brion, Points entiers dans les polyedres convexes, Ann. Sci. Ecole Norm. Sup. (4) 21 (1988), no. 4, 653-663. https://doi.org/10.24033/asens.1572
- M. Brion and M. Vergne, Residue formulae, vector partition functions and lattice points in rational polytopes, J. Amer. Math. Soc. 10 (1997), no. 4, 797-833. https://doi.org/10.1090/S0894-0347-97-00242-7
- J. A. De Loera, R. Hemmecke, J. Tauzer, and R. Yoshida, Effective lattice point counting in rational convex polytopes, J. Symbolic Comput. 38 (2004), no. 4, 1273-1302. https://doi.org/10.1016/j.jsc.2003.04.003
- L. T. Hoa and S. Zarzuela, Reduction number and a-invariant of good filtrations, Comm. Algebra 22 (1994), no. 14, 5635-5656. https://doi.org/10.1080/00927879408825151
- V. Kodiyalam, Homological invariants of powers of an ideal, Proc. Amer. Math. Soc. 118 (1993), no. 3, 757-764. https://doi.org/10.2307/2160118
- E. Miller and B. Sturmfels, Combinatorial Commutative Algebra, Graduate Texts in Mathematics, 227, Springer-Verlag, New York, 2005.
- J. S. Okon and L. J. Ratliff, Jr., Reductions of filtrations, Pacific J. Math. 144 (1990), no. 1, 137-154. http://projecteuclid.org/euclid.pjm/1102645830 https://doi.org/10.2140/pjm.1990.144.137
- L. J. Ratliff, Jr., and D. E. Rush, Two notes on reductions of ideals, Indiana Univ. Math. J. 27 (1978), no. 6, 929-934. https://doi.org/10.1512/iumj.1978.27.27062
- D. Rees, A note on analytically unramified local rings, J. London Math. Soc. 36 (1961), 24-28. https://doi.org/10.1112/jlms/s1-36.1.24
- R. P. Stanley, Combinatorial reciprocity theorems, in Combinatorics, Part 2: Graph theory; foundations, partitions and combinatorial geometry (Proc. Adv. Study Inst., Breukelen, 1974), 107-118. Math. Centre Tracts, 56, Math. Centrum, Amsterdam, 1974.
- B. Sturmfels, On vector partition functions, J. Combin. Theory Ser. A 72 (1995), no. 2, 302-309. https://doi.org/10.1016/0097-3165(95)90067-5