References
- Beck, M., Robins, S. (2015). Computing the Continuous Discretely. In Undergraduate Texts in Mathematics, 2nd ed. New York: Springer.
- Bruns, W., Herzog, J. (1998). Cohen-Macaulay Rings, revised edition. New York: Cambridge University Press.
- De Negri, E., Hibi, T. (1997). Gorenstein algebras of Veronese type. J. Algebra 193(2):629–639. DOI: 10.1006/jabr.1997.6990.
- Diestel, R. (2017). Graph Theory. In Graduate Texts in Mathematics, 173, 5th ed. Berlin: Springer.
- Goto, S., Takahashi, R., Taniguchi, N. (2015). Almost Gorenstein rings – towards a theory of higher dimension. J. Pure Appl. Algebra 219(7):2666–2712. DOI: 10.1016/j.jpaa.2014.09.022.
- Grayson, D., Stillman, M. Macaulay2, a software system for research in algebraic geometry, http://www.math.uiuc.edu/Macaulay2/.
- Herzog, J., Hibi, T., Ohsugi, H. (2018). Binomial ideals. Graduate Texts in Mathematics, 279. Cham: Springer.
- Hibi, T. (1987). Distributive lattices, affine semigroup rings and algebras with straightening laws. In: Nagata, M., Matsumura, H. (eds.) Commutative Algebra and Combinatorics. Advanced Studies in Pure Mathematics, vol. 11. Amsterdam: North-Holland, pp. 93–109.
- Higashitani, A. (2016). Almost Gorenstein homogeneous rings and their h-vectors. J. Algebra 456:190–206. DOI: 10.1016/j.jalgebra.2016.02.023.
- Higashitani, A., Matsushita, K. (2020). Conic divisorial ideals and non-commutative crepant resolutions of edge rings of complete multipartite graphs, arXiv:2011.07714.
- Higashitani, A., Nakajima, Y. (2019). Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions. Selecta Math. 25:25pp.
- Miyazaki, M. (2017). On the generators of the canonical module of a Hibi ring: A criterion of level property and the degrees of generators. J. Algebra 480:215–236. DOI: 10.1016/j.jalgebra.2017.02.011.
- Miyazaki, M. (2018). Almost Gorenstein Hibi rings. J. Algebra 493:135–149. DOI: 10.1016/j.jalgebra.2017.09.033.
- Ohsugi, H., Hibi, T. (1998). Normal polytopes arising from finite graphs. J. Algebra 207(2):409–426. DOI: 10.1006/jabr.1998.7476.
- Ohsugi, H., Hibi, T. (2000). Compressed polytopes, initial ideals and complete multipartite graphs. Illinois J. Math. 44(2):391–406. DOI: 10.1215/ijm/1255984847.
- Simis, A., Vasconcelos, W. V., Villarreal, R. H. (1998). The integral closure of subrings associated to graphs. J. Algebra 199(1):281–289. DOI: 10.1006/jabr.1997.7171.
- Stanley, R. P. (1977). Cohen–Macaulay Complexes, In: M. Aigner (Ed.), Reidel, Dor-drecht and Boston: Higher Combinatorics, p. 51–62.
- Villarreal, R. H. (2015). Monomial algebras. Monographs and Research Notes in Mathematics. Boca Raton, FL: CRC Press.
- Yanagawa, K. (1995). Castelnuovo’s Lemma and h-vectors of Cohen–Macaulay homogeneous domains. J. Pure Appl. Algebra 105(1):107–116. DOI: 10.1016/0022-4049(94)00139-1.