Projects per year
Abstract
We consider digit expansions in lattices with endomorphisms acting as base. We focus on the w-non-adjacent form (w-NAF), where each block of w consecutive digits contains at most one non-zero digit. We prove that for sufficiently large w and an expanding endomorphism, there is a suitable digit set such that each lattice element has an expansion as a w-NAF.
If the eigenvalues of the endomorphism are large enough and w is sufficiently large, then the w-NAF is shown to minimise the weight among all possible expansions of the same lattice element using the same digit system.
If the eigenvalues of the endomorphism are large enough and w is sufficiently large, then the w-NAF is shown to minimise the weight among all possible expansions of the same lattice element using the same digit system.
| Original language | English |
|---|---|
| Pages (from-to) | 90-104 |
| Journal | Acta Mathematica Hungarica |
| Volume | 140 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - 2013 |
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)
- Application
- Theoretical
Fingerprint
Dive into the research topics of 'Existence and Optimality of w-non-adjacent Forms with an Algebraic Integer Base'. Together they form a unique fingerprint.Projects
- 2 Finished
-
Doctoral Program: Discrete Mathematics
Ebner, O. (Co-Investigator (CoI)), Lehner, F. (Co-Investigator (CoI)), Greinecker, F. (Co-Investigator (CoI)), Burkard, R. (Co-Investigator (CoI)), Wallner, J. (Principal Investigator (PI)), Elsholtz, C. (Co-Investigator (CoI)), Woess, W. (Co-Investigator (CoI)), Raseta, M. (Co-Investigator (CoI)), Bazarova, A. (Co-Investigator (CoI)), Krenn, D. (Co-Investigator (CoI)), Lehner, F. (Co-Investigator (CoI)), Kang, M. (Co-Investigator (CoI)), Tichy, R. (Principal Investigator (PI)), Sava-Huss, E. (Co-Investigator (CoI)), Klinz, B. (Principal Investigator (PI)), Heuberger, C. (Principal Investigator (PI)), Grabner, P. (Principal Investigator (PI)), Barroero, F. (Co-Investigator (CoI)), Cuno, J. (Co-Investigator (CoI)), Kreso, D. (Co-Investigator (CoI)), Berkes, I. (Principal Investigator (PI)) & Kerber, M. (Co-Investigator (CoI))
1/05/10 → 30/06/24
Project: Research project
-
Analytic Combinatorics: Analytic Combinatorics and Probabilistic Number Theory
Wagner, S. (Co-Investigator (CoI)), Madritsch, M. (Co-Investigator (CoI)), Aistleitner, C. (Co-Investigator (CoI)), Barat, G. (Co-Investigator (CoI)), Thuswaldner, J. (Principal Investigator (PI)), Grabner, P. (Principal Investigator (PI)), Van De Woestijne, C. E. (Co-Investigator (CoI)), Heuberger, C. (Principal Investigator (PI)), Brauchart, J. (Co-Investigator (CoI)), Berkes, I. (Principal Investigator (PI)), Filipin, A. (Co-Investigator (CoI)), Zeiner, M. (Co-Investigator (CoI)) & Tichy, R. (Principal Investigator (PI))
1/01/06 → 31/07/12
Project: Research project