35
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Regularity of powers of d-sequence (parity) binomial edge ideals of unicycle graphs

ORCID Icon & ORCID Icon
Pages 2598-2615 | Received 11 Mar 2023, Accepted 05 Dec 2023, Published online: 19 Jan 2024

References

  • Amalore Nambi, M., Kumar, N. d-Sequence edge binomials, and regularity of powers of binomial edge ideal of trees. To appear in J. Algebra Appl. arXiv:2209.07218v4. DOI: 10.1142/S0219498824501548,.
  • Beyarslan, S., Hà, H. T., Trung, T. N. (2015). Regularity of powers of forests and cycles. J. Algebraic Combin. 42(4): 1077–1095. DOI: 10.1007/s10801-015-0617-y.
  • Bolognini, D., Macchia, A., Strazzanti, F. (2018). Binomial edge ideals of bipartite graphs. Eur. J. Combin. 70:1–25. DOI: 10.1016/j.ejc.2017.11.004.
  • Cutkosky, S. D., Herzog, J., Trung, N. V. (1999). Asymptotic behaviour of the Castelnuovo-Mumford regularity. Compositio Math. 118(3):243–261. DOI: 10.1023/A:1001559912258.
  • Diaconis, P., Eisenbud, D., Sturmfels, B. (1998). Lattice walks and primary decomposition. Mathematical essays in honour of Gian-Carlo Rota (Cambridge, MA, 1996). Progr. Math. 161:173–193.
  • Eisenbud, D. (1995). Commutative Algebra. With a View Toward Algebraic Geometry. Graduate Texts in Mathematics, 150. New York: Springer-Verlag, xvi + 785 pp.
  • Ene, V., Herzog, J., Hibi, T. (2011). Cohen-Macaulay binomial edge ideals. Nagoya Math. J. 204:57–68. DOI: 10.1017/S0027763000010394.
  • Ene, V., Rinaldo, G., Terai, N. (2021). Powers of binomial edge ideal with quadratic Gröbner bases. Nagoya Math. J. 246:233–255. DOI: 10.1017/nmj.2021.1.
  • Grayson, D. R., Stillman, M. E. Macaulay2, a software system for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2/.
  • Herzog, J., Macchia, A., Saeedi Madani, S., Welker, V. (2015). On the ideal of orthogonal representations of a graph in R2. Adv. Appl. Math. 71:146–173.
  • Herzog, J., Hibi, T., Hreinsdóttir, F., Kahle, T., Rauh, J. (2010). Binomial edge ideals and conditional independence statements. Adv. Appl. Math. 45(3):317–333. DOI: 10.1016/j.aam.2010.01.003.
  • Huneke, C. (1980). On the symmetric and Rees algebra of an ideal generated by a d-sequence. J. Algebra 62(2): 268–275. DOI: 10.1016/0021-8693(80)90179-9.
  • Huneke, C. (1981). Symbolic powers of prime ideals and special graded algebras. Commun. Algebra 9(4):339–366. DOI: 10.1080/00927878108822586.
  • Huneke, C. (1982). The theory of d-sequences and powers of ideals. Adv. Math. 46(3):249–279. DOI: 10.1016/0001-8708(82)90045-7.
  • Jayanthan, A. V., Narayanan, N., Raghavendra Rao, B. V. (2019). Regularity of binomial edge ideals of certain block graphs. Proc. Indian Acad. Sci. Math. Sci. 129(3):Paper No. 36, 10 pp.
  • Jayanthan, A. V., Kumar, A., Sarkar, R. (2020). Regularity of powers of quadratic sequences with applications to binomial ideals. J. Algebra 564:98–118. DOI: 10.1016/j.jalgebra.2020.08.004.
  • Jayanthan, A. V., Kumar, A., Sarkar, R. (2021). Almost complete intersection binomial edge ideals and their Rees algebras. J. Pure Appl. Algebra 225(6):Paper No. 106628, 19 pp. DOI: 10.1016/j.jpaa.2020.106628.
  • Kahle, T., Sarmiento, C., Windisch, T. (2016). Parity binomial edge ideals. J. Algebraic Comb. 44(1):99–117. DOI: 10.1007/s10801-015-0657-3.
  • Kodiyalam, V. (2000). Asymptotic behaviour of Castelnuovo-Mumford regularity. Proc. Amer. Math. Soc. 128(2):407–411. DOI: 10.1090/S0002-9939-99-05020-0.
  • Kumar, A. (2021). Lovász-Saks-Schrijver ideals and parity binomial edge ideals of graphs. Eur. J. Combin. 93:Paper No. 103274, 19 pp. DOI: 10.1016/j.ejc.2020.103274.
  • Kumar, A. (2021). Regularity of parity binomial edge ideals. Proc. Amer. Math. Soc. 149(7):2727–2737. DOI: 10.1090/proc/15434.
  • Kumar, A. (2022). Rees algebra and special fiber ring of binomial edge ideals of closed graphs. Illinois J. Math. 66(1):79–90. DOI: 10.1215/00192082-9702270.
  • Lovász, L., Saks, M., Schrijver, A. (1989). Orthogonal representations and connectivity of graphs. Linear Algebra Appl. 114/115:439–454. DOI: 10.1016/0024-3795(89)90475-8.
  • Mascia, C., Rinaldo, G. (2020). Krull dimension and regularity of binomial edge ideals of block graphs. J. Algebra Appl. 19(7):050133, 17. DOI: 10.1142/S0219498820501339.
  • Matsuda, K., Murai, S. (2013). Regularity bounds for binomial edge ideals. J. Commut. Algebra 5(1):141–149. DOI: 10.1216/JCA-2013-5-1-141.
  • Mohammadi, F., Sharifan, L. (2014). Hilbert function of binomial edge ideals. Commun. Algebra 42(2):688–703. DOI: 10.1080/00927872.2012.721037.
  • Ohtani, M. (2011). Graphs and ideals generated by some 2-minors. Commun. Algebra 39(3):905–917. DOI: 10.1080/00927870903527584.
  • Raghavan, K. (1994). Powers of ideals generated by quadratic sequences. Trans. Amer. Math. Soc. 343(2):727–747. DOI: 10.1090/S0002-9947-1994-1188639-1.
  • Rauh, J., Ay, N. Robustness and conditional independence ideals. arXiv:1110.1338.
  • Rinaldo, G. (2013). Cohen-Macauley binomial edge ideals of small deviation. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 56(104), no. 4:497–503.
  • Sarkar, R. (2021). Binomial edge ideals of unicyclic graphs. Int. J. Algebra Comput. 31(7):129. DOI: 10.1142/S0218196721500466.
  • Shen, Y.-H., Zhu, G. (2023). Regularity of powers of (parity) binomial edge ideals. J. Algebraic Combin. 57(1): 75–100. DOI: 10.1007/s10801-022-01163-w.
  • Villarreal, R. H. (1990). Cohen-Macaulay graphs. Manuscripta Math. 66(3):277–293. DOI: 10.1007/BF02568497.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.