{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:22Z","timestamp":1753893862284,"version":"3.41.2"},"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>Consider these two distinct combinatorial objects: (1) the necklaces of length $n$ with at most $q$ colors, and (2) the multisets of integers modulo $n$ with subset sum divisible by $n$ and with the\u00a0 multiplicity of each element being strictly less than $q$. We show that these two objects have the same cardinality if $q$ and $n$ are mutually coprime. Additionally, when\u00a0 $q$ is a prime power, we construct a bijection between these two objects by viewing\u00a0 necklaces as\u00a0 cyclic polynomials over the finite field of size $q$. Specializing to $q=2$ answers a\u00a0 bijective problem posed by Richard\u00a0 Stanley (Enumerative Combinatorics Vol. 1 Chapter 1, Problem 105(b)).<\/jats:p>","DOI":"10.37236\/7804","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:11:45Z","timestamp":1578640305000},"source":"Crossref","is-referenced-by-count":1,"title":["A Bijection between Necklaces and Multisets with Divisible Subset Sum"],"prefix":"10.37236","volume":"26","author":[{"given":"Swee Hong","family":"Chan","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,3,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p37\/7796","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p37\/7796","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:16:14Z","timestamp":1579234574000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i1p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7804","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,3,8]]},"article-number":"P1.37"}}