EXTREMAL SET THEORY, CUBIC FORMS ON F n 2 AND HURWITZ SQUARE IDENTITIES
Résumé
We study cubic forms on F n 2 using the Hurwitz-Radon theory of square identities. As an application, we obtain the following elementary statement. Given a family F of subsets of an n-set such that the cardinality of the symmetric di↵erence of any two elements F, F 0 2 F is not a multiple of 4, the maximal size of F is bounded by 2n, unless n ⌘ 3 mod 4 when it is bounded by 2n + 2. We also apply this theory to obtain some information about Boolean cubic forms and so-called additive quadruples.
Domaines
Mathématiques [math]
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