References
- [1] L. Amata, M. Crupi, ExteriorIdeals: A package for computing monomial ideals in an exterior algebra, Journal of Software for Algebra and Geometry 8(1) (2018), 71–79.10.2140/jsag.2018.8.71
- [2] L. Amata, M. Crupi, Bounds for the Betti numbers of graded modules with given Hilbert function in an exterior algebra via lexicographic modules, Bull. Math. Soc. Sci. Math. Roumanie, Tome 61(109) No. 3, 237–253, 2018.
- [3] L. Amata, M. Crupi, Hilbert functions of graded modules over exterior algebras: an algorithmic approach, Int. Electron. J. Algebra, Vol. 27, 271–287, 2020.10.24330/ieja.663094
- [4] A. Aramova, J. Herzog, T. Hibi, Gotzman Theorems for Exterior algebra and combinatorics, J. Algebra 191 (1997), 174–211.10.1006/jabr.1996.6903
- [5] A. Aramova, J. Herzog, Almost regular sequence and Betti numbers, Amer.J. Math 122 (2000), 689–719.10.1353/ajm.2000.0025
- [6] W. Bruns, J. Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, Vol. 39, 1998.10.1017/CBO9780511608681
- [7] D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, Vol. 150, Graduate texts in Mathematics, Springer–Verlag, 1995.10.1007/978-1-4612-5350-1
- [8] M. Crupi, C. Ferrò, Bounding Betti numbers of monomial ideals in the exterior algebra, Pure and Appl. Math. Q., 11(2) (2015) 267–281.10.4310/PAMQ.2015.v11.n2.a4
- [9] M. Crupi, C. Ferrò, Squarefree monomial modules and extremal Betti numbers, Algebra Coll. 23 (3) (2016), 519–530.10.1142/S100538671600050X
- [10] W. Decker, G. M. Greuel, G. Pfister, H. Schönemann: Singular 4-1-0 — A computer algebra system for polynomial computations, available at http://www.singular.uni-kl.de (2016).
- [11] V. Gasharov, Extremal properties of Hilbert functions, Illinois J.Math. 41(4) (1997), 612–629.10.1215/ijm/1256068984
- [12] D.R. Grayson, M.E. Stillman, Macaulay2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2.
- [13] M. Crupi, G. Restuccia, Monomial modules and graded Betti numbers, Math. Notes 85 (2009), 690–702.10.1134/S0001434609050095
- [14] J. Herzog, T. Hibi, Monomial ideals, Graduate texts in Mathematics, Vol. 260, Springer–Verlag, 2011.10.1007/978-0-85729-106-6
- [15] A.H. Hoefel, Hilbert functions in monomial algebras, Doctoral Thesis, Dalhousie University, 2011.
- [16] H. Hulett: Maximum Betti numbers for a given Hilbert function, Comm. Algebra 21 (1993), 2335–2350.10.1080/00927879308824680
- [17] H. Hulett, A generalization of Macaulay’s Theorem, Comm. Algebra 23 (1995), 1249–1263.10.1080/00927879508825278
- [18] G. Katona, A theorem for finite sets in “Theory of graphs”, P. Erdös and G. Katona, eds., Academic Press, New York (1968), 187–207.
- [19] J. Kruskal, The number of simplices in a complex, in “Mathematical optimization techniques” (R. Bellman, ed.), University of California Press, Berkeley (1963), 251–278.10.1525/9780520319875-014
- [20] F.S. Macaulay, Some properties of enumeration in the theory of modular systems, Proc. Lond. Math. Soc. 26 (1927), 531–555.10.1112/plms/s2-26.1.531
- [21] R.P. Stanley, Cohen-Macaulay rings and constructible polytopes, Bull. Amer. Math. Soc., 8 (1975), 133–135.10.1090/S0002-9904-1975-13670-6