Maximal Fields Disjoint From Finite Sets
نویسندگان
چکیده
منابع مشابه
Inclusion-maximal integral point sets over finite fields
We consider integral point sets in affine planes over finite fields. Here an integral point set is a set of points in F2q where the formally defined Euclidean distance of every pair of points is an element of Fq. From another point of view we consider point sets over F2q with few and prescribed directions. So this is related to Rédei’s work. Another motivation comes from the field of ordinary i...
متن کاملMaximal integral point sets in affine planes over finite fields
Motivated by integral point sets in the Euclidean plane, we consider integral point sets in affine planes over finite fields. An integral point set is a set of points in the affine plane F2q over a finite field Fq, where the formally defined squared Euclidean distance of every pair of points is a square in Fq. It turns out that integral point sets over Fq can also be characterized as affine poi...
متن کاملDisjoint cliques and disjoint maximal independent sets of vertices in graphs
In this paper, we find lower bounds for the maximum and minimum numbers of cliques in maximal sets of pairwise disjoint cliques in a graph . By complementation, these yield lower bounds for the maximum and minimum numbers of independent sets in maximal sets of pairwise disjoint maximal independent sets of vertices in a graph . In the latter context, we show by examples that one of our bounds is...
متن کاملSome results on maximal open sets
In this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. Some results about existence of maximal m-open setsare given. Moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.Our results are supported by examples and counterexamples.
متن کاملLarge sets in finite fields are sumsets
For a prime p, a subset S of Zp is a sumset if S = A+A for some A ⊂ Zp. Let f(p) denote the maximum integer so that every subset S ⊂ Zp of size at least p− f(p) is a sumset. The question of determining or estimating f(p) was raised by Green. He showed that for all sufficiently large p, f(p) ≥ 19 log2 p and proved, with Gowers, that f(p) < cp 2/3 log p for some absolute constant c. Here we impro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1968
ISSN: 0002-9939
DOI: 10.2307/2036213