Equivariant hilbert series of monomial orbits

Sema Güntürkün; Uwe Nagel

doi:10.1090/proc/13943

Equivariant hilbert series of monomial orbits

Sema Güntürkün, Uwe Nagel

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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	https://doi.org/10.1090/proc/13943
State	Published - 2018

Bibliographical note

Publisher Copyright:
© 2018 Amerian Mathematial Soiety.

Keywords

Degree
Hilbert function
Invariant ideal
Krull dimension
Monoid
Multiplicity
Polynomial ring

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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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 R{\"o}mer is rather efficient.",

keywords = "Degree, Hilbert function, Invariant ideal, Krull dimension, Monoid, Multiplicity, Polynomial ring",

author = "Sema G{\"u}nt{\"u}rk{\"u}n and Uwe Nagel",

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AU - Güntürkün, Sema

AU - Nagel, Uwe

PY - 2018

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N2 - 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.

AB - 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.

KW - Degree

KW - Hilbert function

KW - Invariant ideal

KW - Krull dimension

KW - Monoid

KW - Multiplicity

KW - Polynomial ring

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M3 - Article

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EP - 2393

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -

Equivariant hilbert series of monomial orbits

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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