{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:54:52Z","timestamp":1787320492044,"version":"build-2736575974"},"reference-count":7,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>When numbers are added in base $b$ in the usual way, carries occur. If two random, independent 1-digit numbers are added, then the probability of a carry is $\\frac{b-1}{2b}$. Other choices of digits lead to less carries. In particular, if for odd $b$ we use the digits $\\{-(b-1)\/2, -(b-3)\/2, \\ldots , \\ldots (b-1)\/2\\}$ then the probability of carry is only $\\frac{b^2-1}{4b^2}$. Diaconis, Shao, and Soundararajan conjectured that this is the best choice of digits, and proved that this is asymptotically the case when $b=p$ is a large prime. In this note we prove this conjecture for all odd primes $p$.<\/jats:p>","DOI":"10.1137\/120890612","type":"journal-article","created":{"date-parts":[[2013,3,19]],"date-time":"2013-03-19T11:09:29Z","timestamp":1363691369000},"page":"562-566","source":"Crossref","is-referenced-by-count":3,"title":["Minimizing the Number of Carries in Addition"],"prefix":"10.1137","volume":"27","author":[{"given":"Noga","family":"Alon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,3,19]]},"reference":[{"key":"atypb1","first-page":"639","volume":"47","author":"Borodin A.","year":"2010","journal-title":"S.)"},{"key":"atypb2","first-page":"99","volume":"9","author":"Cauchy A. L.","year":"1813","journal-title":"J. \u00c9cole Polytech."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-10.37.30"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-22.2.100"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-01-10722-9"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-8.3.460"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-11.2.147"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/120890612","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:57:07Z","timestamp":1787317027000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/120890612"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["10.1137\/120890612"],"URL":"https:\/\/doi.org\/10.1137\/120890612","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]}}}