{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:26Z","timestamp":1753893866313,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Denoting the real numbers and the nonnegative integers, respectively, by ${\\bf R}$ and ${\\bf N}$, let $S$ be a subset of ${\\bf N}^n$ for $n = 1, 2,\\ldots$, and $f$ be a mapping from ${\\bf R}^n$ into ${\\bf R}$. We call $f$ a packing function on $S$ if the restriction $f|_{S}$ is a bijection onto ${\\bf N}$.\u00a0For all positive integers $r_1,\\ldots,r_{n-1}$, we consider the\u00a0integer sector \\[I(r_1, \\ldots, r_{n-1}) =\\{(x_1,\\ldots,x_n) \\in N^n \\; | \\; x_{i+1} \\leq \u00a0r_ix_i \\mbox{ for } i = 1,\\ldots,n-1 \\}.\\] Recently,\u00a0Melvyn B. Nathanson (2014) proved that for $n=2$ there exist two quadratic packing polynomials on the sector $I(r)$. Here,\u00a0for $n&gt;2$ we construct $2^{n-1}$ packing polynomials on multidimensional integer sectors.\u00a0In particular, for each packing polynomial on ${\\bf N}^n$ we\u00a0construct a packing polynomial on the sector $I(1, \\ldots, 1)$.<\/jats:p>","DOI":"10.37236\/5299","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:10:26Z","timestamp":1578687026000},"source":"Crossref","is-referenced-by-count":0,"title":["Packing Polynomials  on Multidimensional Integer Sectors"],"prefix":"10.37236","volume":"23","author":[{"given":"Luis B.","family":"Morales","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,10,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:11:38Z","timestamp":1579237898000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i4p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,14]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/5299","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,10,14]]},"article-number":"P4.5"}}