The EGH Conjecture and the Sperner property of complete intersections
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- by Tadahito Harima, Akihito Wachi and Junzo Watanabe PDF
- Proc. Amer. Math. Soc. 145 (2017), 1497-1503 Request permission
Abstract:
Let $A$ be a graded complete intersection over a field and $B$ the monomial complete intersection with the generators of the same degrees as $A$. The EGH conjecture says that if $I$ is a graded ideal in $A$, then there should be an ideal $J$ in $B$ such that $B/J$ and $A/I$ have the same Hilbert function. We show that if the EGH conjecture is true, then it can be used to prove that every graded complete intersection over any field has the Sperner property.References
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Additional Information
- Tadahito Harima
- Affiliation: Department of Mathematics Education, Niigata University, Niigata, 950-2181 Japan
- Email: harima@ed.niigata-u.ac.jp
- Akihito Wachi
- Affiliation: Department of Mathematics, Hokkaido University of Education, Kushiro, 085-8580 Japan
- MR Author ID: 646624
- Email: wachi.akihito@k.hokkyodai.ac.jp
- Junzo Watanabe
- Affiliation: Department of Mathematics, Tokai University, Hiratsuka, 259-1201 Japan
- MR Author ID: 243001
- Email: watanabe.juzno@tokai-u.jp
- Received by editor(s): November 16, 2015
- Received by editor(s) in revised form: June 21, 2016
- Published electronically: October 26, 2016
- Additional Notes: This work was supported by JSPS KAKENHI Grant numbers (C) (15K04812), (C) (23540179).
- Communicated by: Irena Peeva
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1497-1503
- MSC (2010): Primary 13M10; Secondary 13C40
- DOI: https://doi.org/10.1090/proc/13347
- MathSciNet review: 3601542