{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T00:41:02Z","timestamp":1769820062703,"version":"3.49.0"},"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In an unpublished note Golomb proposed a family of \"strange\" recursions of metafibonacci type, parametrized by $k$. Previously we showed that contrary to Golomb's conjecture, for each $k$ there are many increasing solutions, and an explicit construction  for multiple solutions was displayed. By reformulating our solution approach using matrix dynamics, we extend these results to a characterization of the asymptotic behaviour of all solutions of the Golomb recursion. This matrix dynamics perspective is also used to construct what we believe is the first example of a \"nontrivial\" nonincreasing solution, that is, one that is not eventually increasing.<\/jats:p>","DOI":"10.37236\/1301","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:53:44Z","timestamp":1578707624000},"source":"Crossref","is-referenced-by-count":6,"title":["A Matrix Dynamics Approach to Golomb's Recursion"],"prefix":"10.37236","volume":"4","author":[{"given":"Edward J.","family":"Barbeau","sequence":"first","affiliation":[]},{"given":"John","family":"Chew","sequence":"additional","affiliation":[]},{"given":"Stephen","family":"Tanny","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1997,7,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v4i1r16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v4i1r16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:13:59Z","timestamp":1579328039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v4i1r16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,7,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1997,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1301","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,7,14]]},"article-number":"R16"}}