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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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