{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T18:03:12Z","timestamp":1772128992356,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We introduce an infinite class of polynomial sequences $a_t(n;z)$ with integer\u00a0parameter $t\\geq 1$, which reduce to the well-known Stern (diatomic) sequence when $z=1$ and are $(0,1)$-polynomials when $t\\geq 2$.\u00a0Using these polynomial sequences, we derive two different characterizations\u00a0of all hyperbinary expansions of an integer $n\\geq 1$. Furthermore,\u00a0we study the polynomials $a_t(n;z)$ as objects in their own right,\u00a0obtaining a generating function and some consequences. We also prove results on the structure of these sequences, and determine\u00a0expressions for the degrees of the polynomials.<\/jats:p>","DOI":"10.37236\/4822","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:02:24Z","timestamp":1578700944000},"source":"Crossref","is-referenced-by-count":6,"title":["Hyperbinary Expansions and Stern Polynomials"],"prefix":"10.37236","volume":"22","author":[{"given":"Karl","family":"Dilcher","sequence":"first","affiliation":[]},{"given":"Larry","family":"Ericksen","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,5,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:17:19Z","timestamp":1579256239000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i2p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,14]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/4822","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,14]]},"article-number":"P2.24"}}