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Comp."],"abstract":"<p>The summatory function of the number of binomial coefficients not divisible by a prime is known to exhibit regular periodic oscillations, yet identifying the less regularly behaved minimum of the underlying periodic functions has been open for almost all cases. We propose an approach to identify such minimum in some generality, solving particularly a previous conjecture of B.\u00a0Wilson [Acta Arith. 83 (1998), 105\u2013116].<\/p>","DOI":"10.1090\/mcom\/4108","type":"journal-article","created":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T14:46:02Z","timestamp":1750085162000},"page":"1987-2012","source":"Crossref","is-referenced-by-count":0,"title":["Periodic minimum in the count of binomial coefficients not divisible by a prime"],"prefix":"10.1090","volume":"95","author":[{"given":"Hsien-Kuei","family":"Hwang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Svante","family":"Janson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tsung-Hsi","family":"Tsai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2025,6,16]]},"reference":[{"issue":"1-2","key":"1","first-page":"37","article-title":"The number of multinomial coefficients not divided by a prime","volume":"64","author":"Chen, Yong-Gao","year":"1998","journal-title":"Acta Sci. 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Volodin, Distribution of polynomial coefficients congruent modulo \ud835\udc5d^{\ud835\udc41}, Math. Notes 45 (1989), no. 3, 195\u201399.","DOI":"10.1007\/BF01158554"},{"issue":"5","key":"12","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1080\/00150517.1994.12429185","article-title":"Number of multinomial coefficients not divisible by a prime","volume":"32","author":"Volodin, Nikolai A.","year":"1994","journal-title":"Fibonacci Quart.","ISSN":"https:\/\/id.crossref.org\/issn\/0015-0517","issn-type":"print"},{"issue":"2","key":"13","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1090\/S0002-9939-99-05079-0","article-title":"Multinomial coefficients modulo a prime","volume":"127","author":"Volodin, Nikolai A.","year":"1999","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"key":"14","unstructured":"B. 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