Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Separating invariants for multisymmetric polynomials
HTML articles powered by AMS MathViewer

by Artem Lopatin and Fabian Reimers PDF
Proc. Amer. Math. Soc. 149 (2021), 497-508 Request permission


This article studies separating invariants for the ring of multisymmetric polynomials in $m$ sets of $n$ variables over an arbitrary field $\mathbb {K}$. We prove that in order to obtain separating sets it is enough to consider polynomials that depend only on $\lfloor \frac {n}{2} \rfloor + 1$ sets of these variables. This improves a general result by Domokos about separating invariants. In addition, for $n \leq 4$ we explicitly give minimal separating sets (with respect to inclusion) for all $m$ in case $\text {char}(\mathbb {K}) = 0$ or $\text {char}(\mathbb {K}) > n$.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 13A50, 16R30, 20B30
  • Retrieve articles in all journals with MSC (2020): 13A50, 16R30, 20B30
Additional Information
  • Artem Lopatin
  • Affiliation: Department of Mathematics, State University of Campinas, 651 Sergio Buarque de Holanda, 13083-859 Campinas, SP, Brazil
  • MR Author ID: 740650
  • Email: artem\textunderscore
  • Fabian Reimers
  • Affiliation: Department of Mathematics, Technische Universität München, Zentrum Mathematik - M11, Boltzmannstr. 3, 85748 Garching, Germany
  • MR Author ID: 1271373
  • ORCID: 0000-0003-4552-8186
  • Email:
  • Received by editor(s): November 12, 2019
  • Received by editor(s) in revised form: April 9, 2020
  • Published electronically: December 14, 2020
  • Additional Notes: The first author was supported by FAPESP 2019/10821-8. We are grateful for this support.
  • Communicated by: Jerzy Weyman
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 497-508
  • MSC (2020): Primary 13A50, 16R30, 20B30
  • DOI:
  • MathSciNet review: 4198060