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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
DOI: https://doi.org/10.1090/proc/13502
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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Additional Information

Jürgen Herzog
Affiliation: Fakultät für Mathematik, Fachbereich Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany
Email: juergen.herzog@uni-essen.de

Ayesha Asloob Qureshi
Affiliation: Faculty of Engineering and Natural Sciences, Sabancı University, Orta Mahalle, Tuzla 34956, Istanbul, Turkey
Email: aqureshi@sabanciuniv.edu

Akihiro Shikama
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: a-shikama@cr.math.sci.osaka-u.ac.jp

DOI: https://doi.org/10.1090/proc/13502
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