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Communications in Algebra Volume 49, 2021 - Issue 3
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Research Article

On graded Betti numbers of edge rings of deficient complete bipartite graphs

Pavinder SinghDepartment of Mathematics, Central University of Jammu, Jammu and Kashmir, IndiaORCID Iconhttps://orcid.org/0000-0002-2668-9366
ORCID Icon,
Shahnawaz Ahmad RatherDepartment of Mathematics, Central University of Jammu, Jammu and Kashmir, IndiaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-6144-9798
ORCID Icon &
Rohit VermaDepartment of Mathematics, Central University of Jammu, Jammu and Kashmir, IndiaORCID Iconhttps://orcid.org/0000-0002-4323-2907
ORCID Icon
Pages 1186-1194 | Received 15 Jan 2020, Accepted 27 Sep 2020, Published online: 19 Oct 2020

References

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  • Fröberg, R. (1990). On Stanley-Reisner rings. Topics in algebra. Banach Center Publ. 26(2):57–70. Part 2 (Warsaw, 1988), Part 2, PWN, Warsaw. DOI: 10.4064/-26-2-57-70.
  • Grayson, D., Stillman, M. E. Macaulay 2, a software system for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2/.
  • Hochster, M. (1975). Cohen-Macaulay rings, combinatorics, and simplicial complexes. Ring theory II. Proceedings of the Second Conference, University of Oklahoma, Norman, OK, p. 171–223.
  • Jacques, S. Betti numbers of graph idelas. PhD thesis, University of Sheffield, UK.
  • Lyubeznik, G. (1988). The minimal non-Cohen-Macaulay monomial ideals. J. Pure Appl. Algebra 51(3):261–266. DOI: 10.1016/0022-4049(88)90065-5.
  • Rather, S. A., Singh, P. (2019). Graded Betti numbers of crown edge ideals. Commun. Algebra 47(4):1690–1698. DOI: 10.1080/00927872.2018.1513018.
  • Rather, S. A., Singh, P. (2019). On Betti numbers of edge ideals of crown graphs. Beitr. Algebra Geom. 60(1):123–136. DOI: 10.1007/s13366-018-0397-3.
  • Singh, P., Rather, S. A. (2020). On minimal free resolution of edge ideals of multipartite crown graphs. Commun. Algebra 48(3):1314–1326. DOI: 10.1080/00927872.2019.1684505.
  • Wegner, G. (1975). d-collapsing and nerves of families of convex sets. Arch. Math. 26(1):317–321. DOI: 10.1007/BF01229745.
  • Villarreal, R. H. (2015). Monomial Algebras, Monographs and Textbooks in Pure and Applied Mathematics, 2nd ed. Boca Raton, FL: CRC Press.

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