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Communications in Algebra Volume 48, 2020 - Issue 6
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Original Articles

Some interpretations for algebraic invariants of edge ideals of hypergraphs via combinatorial invariants

Somayeh MoradiDepartment of Mathematics, School of Science, Ilam University, Ilam, Iran
&
Fahimeh Khosh-AhangDepartment of Mathematics, School of Science, Ilam University, Ilam, IranCorrespondence[email protected] [email protected]
Pages 2699-2712 | Received 08 Apr 2019, Accepted 05 Dec 2019, Published online: 19 Feb 2020

References

  • Barile, M. (2005). On ideals whose radical is a monomial ideal. Commun. Algebra 33(12):4479–4490. DOI: 10.1080/00927870500274812.
  • Berge, C. (1973). Graphs and Hypergraphs, Vol. 6. (Edward, F., trans.). Amsterdam: North-Holland Publishing Co., xiv + 528 pp.
  • Eliahou, S., Kervaire, M. (1990). Minimal resolutions of some monomial ideals. J. Algebra 129(1):1–25. DOI: 10.1016/0021-8693(90)90237-I.
  • Ha, H. T., Van Tuyl, A. (2008). Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers. J. Algebraic Combin. 27(2):215–245. DOI: 10.1007/s10801-007-0079-y.
  • Hochster, M. (1977). Cohen–Macaulay rings, combinatorics, and simplicial complexes. Presented at the Ring Theory, II (Proceedings of Second Conference, University of Oklahoma, Norman, Oklahoma, 1975). Lecture Notes in Pure Applied Mathematics, Vol. 26. New York: Dekker, pp. 171–223.
  • Katzman, M. (2006). Characteristic-independence of Betti numbers of graph ideals. J. Combin. Theory Ser. A 113(3):435–454. DOI: 10.1016/j.jcta.2005.04.005.
  • Khosh-Ahang, F., Moradi, S. (2014). Regularity and projective dimension of the edge ideal of C5-free vertex decomposable graphs. Proc. Am. Math. Soc. 142(5):1567–1576. DOI: 10.1090/S0002-9939-2014-11906-X.
  • Kimura, K. (2012). Non-vanishingness of Betti numbers of edge ideals. In: Hibi T., ed. Harmony of Gröbner Bases and the Modern Industrial Society. Hackensack, NJ: World Sci. Publ., pp. 153–168.
  • Lyubeznik, G. (1988). A new explicit finite free resolution of ideals generated by monomials in an R-sequence. J. Pure Appl. Algebra 51(1–2):193–195. DOI: 10.1016/0022-4049(88)90088-6.
  • Moradi, S., Khosh-Ahang, F. (2017). Matchings in hypergraphs and Castelnuovo–Mumford regularity. Publ. Math. Debrecen 91(3–4):427–439. DOI: 10.5486/PMD.2017.7755.
  • Morey, S., Villarreal, R. H. (2012). Edge ideals: Algebraic and combinatorial properties. Prog. Commut. Algebra 1:85–126.
  • Villarreal, R. H. (1990). Cohen–Macaulay graphs. Manuscripta Math. 66(1):277–293. DOI: 10.1007/BF02568497.
  • Zheng, X. (2004). Resolutions of facet ideals. Commun. Algebra 32(6):2301–2324. DOI: 10.1081/AGB-120037222.

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