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
- F. Parlamento, A. Policriti, and K. P. S. B. Rao, Witnessing differences without redundancies, Proc. Amer. Math. Soc. 125 (1997), no. 2, 587–594. MR 1353394, DOI 10.1090/S0002-9939-97-03630-7
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