Geodesic
The odd and even intersection properties
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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A non-empty family $\mathscr{S}$ of subsets of a finite set $A$ has the odd (respectively, even) intersection property if there exists non-empty $B \subseteq A$ with $|B \cap S|$ odd (respectively, even) for each $S \in \mathscr{S}$. In characterizing sets of integers that are quadratic non-residues modulo infinitely many primes, Wright asked for the number of such $\mathscr{S}$, as a function of $|A|$. We give explicit formulae.
DOI : 10.37236/672
Classification : 05A15, 11A15
Mots-clés : odd intersection properties 
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     author = {Victor Scharaschkin},
     title = {The odd and even intersection properties},
     journal = {The electronic journal of combinatorics},
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     number = {1},
     doi = {10.37236/672},
     zbl = {1234.05030},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/672/}
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Victor Scharaschkin. The odd and even intersection properties. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/672

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