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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Abelian groups with layered tiles and the sumset phenomenon
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by Renling Jin and H. Jerome Keisler PDF
Trans. Amer. Math. Soc. 355 (2003), 79-97 Request permission

Abstract:

We prove a generalization of the main theorem in Jin, The sumset phenomenon, about the sumset phenomenon in the setting of an abelian group with layered tiles of cell measures. Then we give some applications of the theorem for multi–dimensional cases of the sumset phenomenon. Several examples are given in order to show that the applications obtained are not vacuous and cannot be improved in various directions. We also give a new proof of Shnirel’man’s theorem to illustrate a different approach (which uses the sumset phenomenon) to some combinatorial problems.
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Additional Information
  • Renling Jin
  • Affiliation: Department of Mathematics, College of Charleston, Charleston, South Carollina 29424
  • Email: jinr@cofc.edu
  • H. Jerome Keisler
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • Email: keisler@math.wisc.edu
  • Received by editor(s): October 10, 2001
  • Published electronically: September 6, 2002
  • Additional Notes: The first author’s research is supported in part by NSF grant DMS#0070407.
    The second author’s research is supported in part by Vilas Trust Foundation.
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 79-97
  • MSC (2000): Primary 20K99, 60B15, 22A05, 03H05; Secondary 11B05, 26E35, 28E05
  • DOI: https://doi.org/10.1090/S0002-9947-02-03140-9
  • MathSciNet review: 1928078