English

Minimizing the frequency of carries in modular addition

Number Theory 2015-11-10 v1

Abstract

When adding integers in base mm, carries occur. The same happens modulo a generic integer qq when the set of digits is a complete set of residues modulo mm for some positive integer mm dividing qq. In this paper we prove that asymptotically every digital set in this setting induces carries with frequency at least 1/41/4, thus generalizing results of Alon, Diaconis, Shao and Soundararajan.

Keywords

Cite

@article{arxiv.1511.02404,
  title  = {Minimizing the frequency of carries in modular addition},
  author = {Francesco Monopoli},
  journal= {arXiv preprint arXiv:1511.02404},
  year   = {2015}
}

Comments

16 pages