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