Abstract
The equivariant Hilbert series of an ideal generated by an orbit of a monomial under the action of the monoid Inc(ℕ) of strictly increasing functions is determined. This is used to find the dimension and degree of such an ideal. The result also suggests that the description of the denominator of an equivariant Hilbert series of an arbitrary Inc(ℕ)-invariant ideal as given by Nagel and Römer is rather efficient.
| Original language | English |
|---|---|
| Pages (from-to) | 2381-2393 |
| Number of pages | 13 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 146 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Publisher Copyright:© 2018 Amerian Mathematial Soiety.
Funding
Received by the editors August 22, 2016, and, in revised form, August 31, 2017. 2010 Mathematics Subject Classification. Primary 13F20, 13A02, 13D40, 13A50. Key words and phrases. Hilbert function, polynomial ring, monoid, invariant ideal, Krull dimension, degree, multiplicity. The second author was partially supported by Simons Foundation grant #317096. The authors are grateful to the referee for a very careful reading of the manuscript.
| Funders | Funder number |
|---|---|
| Simons Foundation | 317096 |
Keywords
- Degree
- Hilbert function
- Invariant ideal
- Krull dimension
- Monoid
- Multiplicity
- Polynomial ring
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics