{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T20:33:10Z","timestamp":1773261190734,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper, we introduce the notion of $q$-quasiadditivity of arithmetic functions, as well as the related concept of $q$-quasimultiplicativity, which generalise strong $q$-additivity and -multiplicativity, respectively. We show that there are many natural examples for these concepts, which are characterised by functional equations of the form $f(q^{k+r}a + b) = f(a) + f(b)$ or $f(q^{k+r}a + b) = f(a) f(b)$ for all $b &lt; q^k$ and a fixed parameter $r$. In addition to some elementary properties of $q$-quasiadditive and $q$-quasimultiplicative functions, we prove characterisations of $q$-quasiadditivity and $q$-quasimultiplicativity for the special class of $q$-regular functions. The final main result provides a general central limit theorem that includes both classical and new examples as corollaries.<\/jats:p>","DOI":"10.37236\/6373","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:59:00Z","timestamp":1578671940000},"source":"Crossref","is-referenced-by-count":4,"title":["On $q$-Quasiadditive and $q$-Quasimultiplicative Functions"],"prefix":"10.37236","volume":"24","author":[{"given":"Sara","family":"Kropf","sequence":"first","affiliation":[]},{"given":"Stephan","family":"Wagner","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p60\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p60\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:03:07Z","timestamp":1579237387000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i1p60"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1,20]]}},"URL":"https:\/\/doi.org\/10.37236\/6373","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,31]]},"article-number":"P1.60"}}