mirage

Cyclotomic integers and finite geometry.

DSpace/Manakin Repository

 

Search DR-NTU


Advanced Search Subject Search

Browse

My Account

Cyclotomic integers and finite geometry.

Show full item record

Title: Cyclotomic integers and finite geometry.
Author: Bernhard, Schmidt.
Copyright year: 1999
Abstract: We obtain an upper bound for the absolute value of cyclotomic integers which has strong implications on several combinatorial structures including (relative) difference sets, quasiregular projective planes, planar functions, and group invariant weighing matrices. Our results are of broader applicability than all previously known nonexistence theorems for these combinatorial objects. We will show that the exponent of an abelian group G containing a (v,k,ג,n)-difference set cannot exceed ((2^(s-1).F(v,n))/n)^0.5where is the number of odd prime divisors of v and F(v,n) is a number-theoretic parameter whose order of magnitude usually is the squarefree part of . One of the consequences is that for any finite set P of primes there is a constant C such that exp(G) ≤ C|G|^0.5for any abelian group G containing a Hadamard difference set whose order is a product of powers of primes in P. Furthermore, we are able to verify Ryser's conjecture for most parameter series of known difference sets. This includes a striking progress towards the circulant Hadamard matrix conjecture. A computer search shows that there is no Barker sequence of length l with 13< l <4x10^12. Finally, we obtain new necessary conditions for the existence of quasiregular projective planes and group invariant weighing matrices including asymptotic exponent bounds for cases which previously had been completely intractable.
Subject: DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics.
Type: Journal Article
Series/ Journal Title: Journal of american mathematical society
School: School of Physical and Mathematical Sciences
Rights: Journal of American Mathematical Society © copyright 1999 American Mathematical Society. The journal's website is located at http://www.ams.org/jams/1999-12-04/S0894-0347-99-00298-2/S0894-0347-99-00298-2.pdf.
Version: Published version

Files in this item

Files Size Format View Description
exp.pdf 336.6Kb PDF View/Open Published version
   

DOI Query

- Get published version (via Digital Object Identifier)
   

This item appears in the following Collection(s)

Show full item record

Statistics

Total views

All Items Views
Cyclotomic integers and finite geometry. 379

Total downloads

All Bitstreams Views
exp.pdf 101

Top country downloads

Country Code Views
United States of America 51
Singapore 20
Russian Federation 7
Japan 6
Unknown Country 5

Top city downloads

city Views
Mountain View 39
Singapore 20
Redwood City 2
Southampton 2
Davidson 1

Downloads / month

  2014-05 2014-06 2014-07 total
exp.pdf 0 0 3 3