On Sidon sequences of even orders
نویسندگان
چکیده
منابع مشابه
Results on Sidon and B h Sequences
Results on Sidon and Bh Sequences Sangjune Lee A set A of non-negative integers is a Sidon set if all the sums a1 + a2, with a1 ≤ a2 and a1, a2 ∈ A, are distinct. In this dissertation, we deal with results on the number of Sidon sets in [n] = {0, 1, · · · , n − 1} and the maximum size of Sidon sets in sparse random subsets of [n] or N (the set of natural numbers). We also consider a natural gen...
متن کاملA note on weak Sidon sequences
A sequence (ai) of integers is weak Sidon or well-spread if the sums ai + aj , for i < j , are all different. Let f (N) denote the maximum integer n for which there exists a weak Sidon sequence 0 a1< · · ·<an N . Using an idea of Lindström [An inequality for B2-sequences, J. Combin. Theory 6 (1969) 211–212], we offer an alternate proof that f (N)<N1/2 + O(N1/4), an inequality due to Ruzsa [Solv...
متن کاملInfinite Sidon sequences
We give the first explicit construction of an infinite Sidon sequence A with A(x) x for some c > 1/3. Our method allows to take c = √ 2− 1. Ruzsa proved the existence of a Sidon sequence with similar counting function but his proof was not constructive. Our method generalizes to Bh sequences when h ≥ 3. In these case our constructions are not explicit but they give the first improvements on the...
متن کاملRandom Sidon Sequences
A subset A of the set [n] = f1; 2; : : : ; ng, jAj = k, is said to form a Sidon (or Bh) sequence, h 2, if each of the sums a1 + a2 + : : : + ah; a1 a2 : : : ah; ai 2 A, are distinct. We investigate threshold phenomena for the Sidon property, showing that if An is a random subset of [n], then the probability that An is a Bh sequence tends to unity as n ! 1 if kn = jAnj n1=2h, and that P(An is Si...
متن کاملEven dimensional higher class groups of orders
Let F be a number field, and let OF denote the ring of integers in F . Let A be a finite-dimensional central simple F-algebra, and let be an OF -order in A. In this paper it is shown that the p-torsion of the even dimensional higher class group Cl2n( ) can only occur for primes p, which lie under prime ideals p, at which p is not maximal, or which divide the dimension of A.
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: Acta Arithmetica
سال: 1993
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-64-4-325-330