## Betti tables of monomial ideals fixed by permutations of the variables

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- by Satoshi Murai PDF
- Trans. Amer. Math. Soc.
**373**(2020), 7087-7107 Request permission

## Abstract:

Let $S_n$ be a polynomial ring with $n$ variables over a field and $\{I_n\}_{n \geq 1}$ a chain of ideals such that each $I_n$ is a monomial ideal of $S_n$ fixed by permutations of the variables. In this paper, we present a way to determine all nonzero positions of Betti tables of $I_n$ for all large intergers $n$ from the $\mathbb Z^m$-graded Betti tables of $I_m$ for some small integers $m$. Our main result shows that the projective dimension and the regularity of $I_n$ eventually become linear functions on $n$, confirming a special case of conjectures posed by Le, Nagel, Nguyen and Römer.## References

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## Additional Information

**Satoshi Murai**- Affiliation: Department of Mathematics, Faculty of Education, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku, Tokyo 169-8050, Japan
- MR Author ID: 800440
- Email: s-murai@waseda.jp
- Received by editor(s): August 5, 2019
- Received by editor(s) in revised form: January 7, 2020
- Published electronically: August 5, 2020
- Additional Notes: The research of the author was partially supported by KAKENHI 16K05102.
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**373**(2020), 7087-7107 - MSC (2010): Primary 13D02; Secondary 13A50
- DOI: https://doi.org/10.1090/tran/8159
- MathSciNet review: 4155201