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On the relations of isotonian algebras

Authors: Jürgen Herzog, Ayesha Asloob Qureshi and Akihiro Shikama
Journal: Proc. Amer. Math. Soc. 145 (2017), 4119-4126
MSC (2010): Primary 05E45, 05E40, 13C99
Published electronically: June 9, 2017
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Abstract: It is shown that for large classes of posets $ P$ and $ Q$, the defining ideal $ J_{P,Q}$ of an isotonian algebra is generated by squarefree binomials. Within these classes, those posets are classified for which $ J_{P,Q}$ is quadratically generated.

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  • [1] M. Bigdeli, J. Herzog, T. Hibi, A. Shikama, and A. A. Qureshi, Isotonian algebras, arXiv:1512.01973
  • [2] G. Fløystad, B. M. Greve, and J. Herzog, Letterplace and co-letterplace ideals of posets.
  • [3] Viviana Ene, Jürgen Herzog, and Fatemeh Mohammadi, Monomial ideals and toric rings of Hibi type arising from a finite poset, European J. Combin. 32 (2011), no. 3, 404-421. MR 2764804,
  • [4] Jürgen Herzog and Takayuki Hibi, Monomial ideals, Graduate Texts in Mathematics, vol. 260, Springer-Verlag London, Ltd., London, 2011. MR 2724673
  • [5] Jürgen Herzog, Ayesha Asloob Qureshi, and Akihiro Shikama, Alexander duality for monomial ideals associated with isotone maps between posets, J. Algebra Appl. 15 (2016), no. 5, 1650089, 6. MR 3479448,
  • [6] Takayuki Hibi, Distributive lattices, affine semigroup rings and algebras with straightening laws, Commutative algebra and combinatorics (Kyoto, 1985) Adv. Stud. Pure Math., vol. 11, North-Holland, Amsterdam, 1987, pp. 93-109. MR 951198
  • [7] Viviana Ene, Jürgen Herzog, and Sara Saeedi Madani, A note on the regularity of Hibi rings, Manuscripta Math. 148 (2015), no. 3-4, 501-506. MR 3414489,
  • [8] Martina Juhnke-Kubitzke, Lukas Katthän, and Sara Saeedi Madani, Algebraic properties of ideals of poset homomorphisms, J. Algebraic Combin. 44 (2016), no. 3, 757-784. MR 3552906,
  • [9] G. Fløystad and A. Nematbakhsh, Rigid ideals by deforming quadratic letterplace ideals.
  • [10] A. D'Alí, G. Fløystad, and A. Nematbakhsh, Resolutions of co-letterplace ideals and generalizations of Bier spheres. arXiv:1601.02793
  • [11] A. D'Alí, G. Fløystad, and A. Nematbakhsh, Resolutions of letterplace ideals of posets. J. Algebr. Comb. (2016). doi:10.1007/s10801-016-0729-z

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Additional Information

Jürgen Herzog
Affiliation: Fakultät für Mathematik, Fachbereich Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany

Ayesha Asloob Qureshi
Affiliation: Faculty of Engineering and Natural Sciences, Sabancı University, Orta Mahalle, Tuzla 34956, Istanbul, Turkey

Akihiro Shikama
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan

Received by editor(s): September 6, 2016
Published electronically: June 9, 2017
Additional Notes: This paper was partially written during the stay of the second author at The Abdus Salam International Centre of Theoretical Physics (ICTP), Trieste, Italy
Communicated by: Irena Peeva
Article copyright: © Copyright 2017 American Mathematical Society

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