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Equivariant Hilbert series of monomial orbits


Authors: Sema Güntürkün and Uwe Nagel
Journal: Proc. Amer. Math. Soc. 146 (2018), 2381-2393
MSC (2010): Primary 13F20, 13A02, 13D40, 13A50
DOI: https://doi.org/10.1090/proc/13943
Published electronically: February 16, 2018
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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 $ {\textrm {Inc} (\mathbb{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 $ {\textrm {Inc} (\mathbb{N})}$-invariant ideal as given by Nagel and Römer is rather efficient.


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Additional Information

Sema Güntürkün
Affiliation: Department of Mathematics, University of Michigan, 530 Church Street, East Hall, Ann Arbor, Michigan 48109
Email: gunturku@umich.edu

Uwe Nagel
Affiliation: Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506-0027
Email: uwe.nagel@uky.edu

DOI: https://doi.org/10.1090/proc/13943
Keywords: Hilbert function, polynomial ring, monoid, invariant ideal, Krull dimension, degree, multiplicity
Received by editor(s): August 22, 2016
Received by editor(s) in revised form: August 31, 2017
Published electronically: February 16, 2018
Additional Notes: 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.
Communicated by: Irena Peeva
Article copyright: © Copyright 2018 American Mathematical Society

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