Cyclotomy and addition sets
نویسندگان
چکیده
منابع مشابه
Difference systems of sets and cyclotomy
Difference Systems of Sets (DSS) are combinatorial configurations that arise in connection with code synchronization. A method for the construction of DSS from partitions of cyclic difference sets was introduced in [6] and applied to cyclic difference sets (n, (n−1)/2, (n−3)/4) of Paley type, where n ≡ 3 (mod 4) is a prime number. This paper develops similar constructions for prime numbers n ≡ ...
متن کاملCyclotomy, Gauss Sums, Difference Sets and Strongly Regular Cayley Graphs
We survey recent results on constructions of difference sets and strongly regular Cayley graphs by using union of cyclotomic classes of finite fields. Several open problems are raised.
متن کاملAddition and multiplication of sets
Ordinal addition and multiplication can be extended in a natural way to all sets. I survey the structure of the sets under these operations. In particular, the natural partial ordering associated with addition of sets is shown to be a tree. This allows us to prove that any set has a unique representation as a sum of additively irreducible sets, and that the non-empty elements of any model of se...
متن کاملCyclotomy and Endomotives
We compare two different models of noncommutative geometry of the cyclotomic tower, both based on an arithmetic algebra of functions of roots of unity and an action by endomorphisms, the first based on the Bost-Connes (BC) quantum statistical mechanical system and the second on the Habiro ring, where the Habiro functions have, in addition to evaluations at roots of unity, also full Taylor expan...
متن کاملCyclotomy and Delta Units
In this paper we examine cyclic cubic, quartic, and quintic number fields of prime conductor p containing units that bear a special relationship to the classical Gaussian periods: n¡ nj+x + c is a unit for periods r\¡ and c e Z.
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: Journal of Combinatorial Theory, Series A
سال: 1977
ISSN: 0097-3165
DOI: 10.1016/0097-3165(77)90062-0