Edge rings with $3$-linear resolutions
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- by Takayuki Hibi, Kazunori Matsuda and Akiyoshi Tsuchiya PDF
- Proc. Amer. Math. Soc. 147 (2019), 3225-3232 Request permission
Abstract:
It is shown that the edge ring of a finite connected simple graph with a $3$-linear resolution is a hypersurface.References
- W. Bruns and J. Herzog, Cohen-Macaulay Rings, revised ed., Cambridge Stud. Adv. Math., vol. 39, Cambridge University Press, Cambridge, 1998.
- David Eisenbud and Shiro Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), no. 1, 89–133. MR 741934, DOI 10.1016/0021-8693(84)90092-9
- Jürgen Herzog and Takayuki Hibi, Monomial ideals, Graduate Texts in Mathematics, vol. 260, Springer-Verlag London, Ltd., London, 2011. MR 2724673, DOI 10.1007/978-0-85729-106-6
- Takayuki Hibi, Algebraic combinatorics on convex polytopes, Carslaw Publications, Glebe, 1992. MR 3183743
- Johannes Hofscheier, Lukas Katthän, and Benjamin Nill, Ehrhart theory of spanning lattice polytopes, Int. Math. Res. Not. IMRN 19 (2018), 5947–5973. MR 3867398, DOI 10.1093/imrn/rnx065
- Hidefumi Ohsugi and Takayuki Hibi, Normal polytopes arising from finite graphs, J. Algebra 207 (1998), no. 2, 409–426. MR 1644250, DOI 10.1006/jabr.1998.7476
- Hidefumi Ohsugi and Takayuki Hibi, Toric ideals generated by quadratic binomials, J. Algebra 218 (1999), no. 2, 509–527. MR 1705794, DOI 10.1006/jabr.1999.7918
- Richard P. Stanley, A monotonicity property of $h$-vectors and $h^*$-vectors, European J. Combin. 14 (1993), no. 3, 251–258. MR 1215335, DOI 10.1006/eujc.1993.1028
- Bernd Sturmfels, Gröbner bases and convex polytopes, University Lecture Series, vol. 8, American Mathematical Society, Providence, RI, 1996. MR 1363949, DOI 10.1090/ulect/008
Additional Information
- Takayuki Hibi
- Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
- MR Author ID: 219759
- Email: hibi@math.sci.osaka-u.ac.jp
- Kazunori Matsuda
- Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
- Address at time of publication: Kazunori Matsuda, Kitami Institute of Technology, Kitami, Hokkaido 090-8507, Japan
- MR Author ID: 912045
- Email: kaz-matsuda@mail.kitami-it.ac.jp
- Akiyoshi Tsuchiya
- Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
- MR Author ID: 1126485
- Email: a-tsuchiya@ist.osaka-u.ac.jp
- Received by editor(s): December 18, 2017
- Received by editor(s) in revised form: August 8, 2018
- Published electronically: May 8, 2019
- Additional Notes: The authors were partially supported by JSPS KAKENHI 26220701, 17K14165, and 16J01549.
- Communicated by: Jerzy Weyman
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3225-3232
- MSC (2010): Primary 05E40, 13H10, 52B20
- DOI: https://doi.org/10.1090/proc/14382
- MathSciNet review: 3981103