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Betti tables of monomial ideals fixed by permutations of the variables
- Source :
- Transactions of the American Mathematical Society. 373:7087-7107
- Publication Year :
- 2020
- Publisher :
- American Mathematical Society (AMS), 2020.
-
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 table of $I_m$ for some integer $m$. 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 R\"omer.<br />Comment: 20 pages
- Subjects :
- Monomial
Mathematics::Combinatorics
Mathematics::Commutative Algebra
Applied Mathematics
General Mathematics
Polynomial ring
010102 general mathematics
Dimension (graph theory)
Field (mathematics)
Monomial ideal
Commutative Algebra (math.AC)
Mathematics - Commutative Algebra
Table (information)
01 natural sciences
Combinatorics
Integer
FOS: Mathematics
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 10886850 and 00029947
- Volume :
- 373
- Database :
- OpenAIRE
- Journal :
- Transactions of the American Mathematical Society
- Accession number :
- edsair.doi.dedup.....508fc25713f18629018500f52c12ad1b