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arXiv · 1511.02404

Minimizing the frequency of carries in modular addition

Francesco Monopoli
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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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Francesco Monopoli. 2015-11-07. Minimizing the frequency of carries in modular addition. https://arxiv.org/abs/1511.02404

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