Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Light matrices of prime determinant


Authors: Daniel Goldstein, Alfred W. Hales and Richard A. Stong
Journal: Proc. Amer. Math. Soc. 142 (2014), 805-819
MSC (2010): Primary 20D05; Secondary 68W30, 11Y16, 15B36
Published electronically: December 4, 2013
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For $ A = \left (a_{i,j}\right )$ a square integer matrix of prime determinant $ p$, set

$\displaystyle w(A)=\sum _{i,j}\left \vert a_{i,j}\right \vert.$

We are interested in the smallest possible value $ w_p$ for $ w(A),$ and we show that

$\displaystyle \lim _{p\rightarrow \infty } w_p/\log _2(p)=5/2.$

We also show that $ w_p \leq 2.5 \log _2(p)$ if and only if $ p=2,7,13,37$ or a Fermat prime. Our results can also be interpreted as being about addition chains or about presentations of finite cyclic groups.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20D05, 68W30, 11Y16, 15B36

Retrieve articles in all journals with MSC (2010): 20D05, 68W30, 11Y16, 15B36


Additional Information

Daniel Goldstein
Affiliation: Center for Communications Research, San Diego, California 92121-1969
Email: dgoldste@ccrwest.org

Alfred W. Hales
Affiliation: Center for Communications Research, San Diego, California 92121-1969
Email: hales@ccrwest.org

Richard A. Stong
Affiliation: Center for Communications Research, San Diego, California 92121-1969
Email: stong@ccrwest.org

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11812-5
PII: S 0002-9939(2013)11812-5
Keywords: Addition chains, presentations
Received by editor(s): April 18, 2011
Received by editor(s) in revised form: April 11, 2012
Published electronically: December 4, 2013
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2013 Institute for Defense Analyses