{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,26]],"date-time":"2025-04-26T09:05:58Z","timestamp":1745658358173},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p> Let S be a numerical monoid with minimal generating set \u3008n<jats:sub>1<\/jats:sub>, \u2026, n<jats:sub>t<\/jats:sub>\u3009. For m \u2208 S, if [Formula: see text], then [Formula: see text] is called a factorization length of m. We denote by \u2112(m) = {m<jats:sub>1<\/jats:sub>, \u2026, m<jats:sub>k<\/jats:sub>} (where m<jats:sub>i<\/jats:sub> &lt; m<jats:sub>i+1<\/jats:sub> for each 1 \u2264 i &lt; k) the set of all possible factorization lengths of m. The Delta set of m is defined by \u0394(m) = {m<jats:sub>i+1<\/jats:sub> - m<jats:sub>i<\/jats:sub> | 1 \u2264 i &lt; k} and the Delta set of S by \u0394(S) = \u22c3<jats:sub>m\u2208S<\/jats:sub>\u0394(m). In this paper, we expand on the study of \u0394(S) begun in [C. Bowles, S. T. Chapman, N. Kaplan and D. Reiser, On delta sets of numerical monoids, J. Algebra Appl.\u00a05 (2006) 1\u201324] in the following manner. Let r<jats:sub>1<\/jats:sub>, r<jats:sub>2<\/jats:sub>, \u2026, r<jats:sub>t<\/jats:sub> be an increasing sequence of positive integers and M<jats:sub>n<\/jats:sub> = \u3008n, n + r<jats:sub>1<\/jats:sub>, n + r<jats:sub>2<\/jats:sub>, \u2026, n + r<jats:sub>t<\/jats:sub>\u3009 a numerical monoid where n is some positive integer. We prove that there exists a positive integer N such that if n &gt; N then |\u0394(M<jats:sub>n<\/jats:sub>)| = 1. If t = 2 and r<jats:sub>1<\/jats:sub> and r<jats:sub>2<\/jats:sub> are relatively prime, then we determine a value for N which is sharp. <\/jats:p>","DOI":"10.1142\/s0218196714500271","type":"journal-article","created":{"date-parts":[[2014,7,2]],"date-time":"2014-07-02T02:58:05Z","timestamp":1404269885000},"page":"655-669","source":"Crossref","is-referenced-by-count":13,"title":["Shifts of generators and delta sets of numerical monoids"],"prefix":"10.1142","volume":"24","author":[{"given":"S. T.","family":"Chapman","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Sam Houston State University, Box 2206, Huntsville, TX 77341-2206, USA"}]},{"given":"Nathan","family":"Kaplan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Princeton University, Princeton NJ 08544-1000, USA"}]},{"given":"Tyler","family":"Lemburg","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Nebraska at Lincoln, 203 Avery Hall, Lincoln, NE 68588-0130, USA"}]},{"given":"Andrew","family":"Niles","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Rochester, Hylan Building, Rochester, NY 14627, USA"}]},{"given":"Christina","family":"Zlogar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY 14853-4201, USA"}]}],"member":"219","published-online":{"date-parts":[[2014,9,3]]},"reference":[{"key":"rf1","volume":"7","author":"Amos J.","year":"2007","journal-title":"Integers"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498806001958"},{"key":"rf4","volume-title":"Finitely Generated Commutative Monoids","author":"Garc\u00eda-S\u00e1nchez P. A.","year":"1999"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1080\/00927879108824164"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1201\/9781420003208"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198568209.001.0001"},{"key":"rf8","first-page":"171","volume":"41","author":"Sylvester J. J.","year":"1884","journal-title":"Educational Times"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196714500271","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:29:16Z","timestamp":1565108956000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196714500271"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8]]},"references-count":7,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2014,9,3]]},"published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.1142\/S0218196714500271"],"URL":"https:\/\/doi.org\/10.1142\/s0218196714500271","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8]]}}}