{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T15:49:04Z","timestamp":1761752944160,"version":"build-2065373602"},"reference-count":0,"publisher":"University of Calgary","issue":"2","license":[{"start":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:00:00Z","timestamp":1761609600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Contrib Discrete Math"],"abstract":"<jats:p>Agarwal defined $n$-colour compositions as ordered $n$-colour partitions in 2000. In this paper, we relate $n$-colour compositions with a problem of sewage water treatment using a bijection which involves the well-known Fibonacci numbers. In addition, we study a new restricted $n$-colour composition function combinatorially. Our work also includes a one-to-one correspondence between restricted $n$-colour compositions and the number of ways to tile a particular type of rectangle using dominoes and squares.<\/jats:p>","DOI":"10.55016\/ojs\/cdm.v20i2.79510","type":"journal-article","created":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T15:44:51Z","timestamp":1761752691000},"page":"497-507","source":"Crossref","is-referenced-by-count":0,"title":["Fibonacci numbers and n-color compositions"],"prefix":"10.55016","volume":"20","author":[{"given":"Rachna","family":"Sachdeva","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Bharti Gupta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Urvashi","family":"Sharma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"13844","published-online":{"date-parts":[[2025,10,28]]},"container-title":["Contributions to Discrete Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/cdm.ucalgary.ca\/article\/download\/79510\/58577","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/cdm.ucalgary.ca\/article\/download\/79510\/58577","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T15:44:52Z","timestamp":1761752692000},"score":1,"resource":{"primary":{"URL":"https:\/\/cdm.ucalgary.ca\/article\/view\/79510"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,28]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,10,28]]}},"URL":"https:\/\/doi.org\/10.55016\/ojs\/cdm.v20i2.79510","relation":{},"ISSN":["1715-0868"],"issn-type":[{"value":"1715-0868","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,28]]}}}