{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T07:46:36Z","timestamp":1648885596661},"reference-count":17,"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":[[2021,8]]},"abstract":"<jats:p> A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. Some of the key properties of a numerical semigroup are its Frobenius number [Formula: see text], genus [Formula: see text] and type [Formula: see text]. It is known that for any numerical semigroup [Formula: see text]. Numerical semigroups with [Formula: see text] are called almost symmetric, we introduce a new property that characterizes them. We give an explicit characterization of numerical semigroups with [Formula: see text]. We show that for a fixed [Formula: see text] the number of numerical semigroups with Frobenius number [Formula: see text] and type [Formula: see text] is eventually constant for large [Formula: see text]. The number of numerical semigroups with genus [Formula: see text] and type [Formula: see text] is also eventually constant for large [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196721500417","type":"journal-article","created":{"date-parts":[[2021,5,18]],"date-time":"2021-05-18T10:26:51Z","timestamp":1621333611000},"page":"883-902","source":"Crossref","is-referenced-by-count":0,"title":["Numerical semigroups of small and large type"],"prefix":"10.1142","volume":"31","author":[{"given":"Deepesh","family":"Singhal","sequence":"first","affiliation":[{"name":"University of California, Irvine, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,5,18]]},"reference":[{"key":"S0218196721500417BIB001","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2001.8994"},{"key":"S0218196721500417BIB002","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-12304"},{"key":"S0218196721500417BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-018-9922-9"},{"key":"S0218196721500417BIB004","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.6837"},{"key":"S0218196721500417BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498819502177"},{"key":"S0218196721500417BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2012.03.011"},{"key":"S0218196721500417BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-009-9175-8"},{"key":"S0218196721500417BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573091"},{"key":"S0218196721500417BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-019-10007-2"},{"key":"S0218196721500417BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2016.02.019"},{"key":"S0218196721500417BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-012-9397-z"},{"key":"S0218196721500417BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-013-9486-7"},{"key":"S0218196721500417BIB014","first-page":"2499","volume":"43","author":"Ojeda I.","year":"2020","journal-title":"Turkish J. Math."},{"key":"S0218196721500417BIB015","series-title":"Developments in Mathematics","volume-title":"Numerical Semigroups","volume":"20","author":"Rosales J. C.","year":"2010"},{"key":"S0218196721500417BIB016","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2012.740117"},{"key":"S0218196721500417BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-002-0007-3"},{"key":"S0218196721500417BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-40822-0_19"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196721500417","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,4]],"date-time":"2021-08-04T06:37:27Z","timestamp":1628059047000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196721500417"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,18]]},"references-count":17,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["10.1142\/S0218196721500417"],"URL":"https:\/\/doi.org\/10.1142\/s0218196721500417","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,18]]}}}