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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

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Finite families with few symmetric differences
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by Alberto Marcone, Franco Parlamento and Alberto Policriti PDF
Proc. Amer. Math. Soc. 127 (1999), 835-845 Request permission

Abstract:

We show that $2^{\lceil \log _2 (m) \rceil }$ is the least number of symmetric differences that a family of $m$ sets can produce. Furthermore we give two characterizations of the set-theoretic structure of the families for which that lower bound is actually attained.
References
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Additional Information
  • Alberto Marcone
  • Affiliation: Dipartimento di Matematica Università di Torino via Carlo Alberto 10 10123 Torino Italy
  • Address at time of publication: Dipartimento di Matematica e Informatica, Università di Udine, viale delle Scienze, 33100 Udine, Italy
  • Email: marcone@dm.unito.it, marcone@dimi.uniud.it
  • Franco Parlamento
  • Affiliation: Dipartimento di Matematica e Informatica Università di Udine viale delle Scienze 33100 Udine Italy
  • Email: parlamen@dimi.uniud.it
  • Alberto Policriti
  • Email: policrit@dimi.uniud.it
  • Received by editor(s): September 27, 1996
  • Additional Notes: This work has been supported by funds 40% and 60% MURST
  • Communicated by: Andreas R. Blass
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 835-845
  • MSC (1991): Primary 04A03; Secondary 90D46
  • DOI: https://doi.org/10.1090/S0002-9939-99-04751-6
  • MathSciNet review: 1487324