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Proceedings of the American Mathematical Society

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

 

 

Finite families with few symmetric differences


Authors: Alberto Marcone, Franco Parlamento and Alberto Policriti
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
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-99-04751-6
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
Article copyright: © Copyright 1999 American Mathematical Society