{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T13:52:40Z","timestamp":1772632360970,"version":"3.50.1"},"reference-count":0,"publisher":"University of Calgary","issue":"1","license":[{"start":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T00:00:00Z","timestamp":1772150400000},"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>Let $S_r(p,q)$ be the $r$-associated Stirling numbers of the second kind, the number of ways to partition a set of size $p$ into $q$ subsets of size at least $r$. For $r=1$, these are the standard Stirling numbers of the second kind, and for $r=2$, these are also known as the Ward Numbers. This paper concerns asymptotic expansions of these Stirling numbers; such expansions have been known for many years.\n\nHowever, while uniform convergence of these expansions was conjectured by Hennecart, it has not been fully proved. A recent paper by Connamacher and Dobrosotskaya went a long way by proving uniform convergence on a large set. In this paper, we build on that paper and prove convergence \"everywhere\".<\/jats:p>","DOI":"10.55016\/dptxws28","type":"journal-article","created":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T07:00:31Z","timestamp":1772434831000},"page":"227-244","source":"Crossref","is-referenced-by-count":0,"title":["Uniform convergence of an asymptotic approximation to associated Stirling numbers"],"prefix":"10.55016","volume":"21","author":[{"given":"E. Rodney","family":"Canfield","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jared","family":"Hughes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7716-3903","authenticated-orcid":false,"given":"J. William","family":"Helton","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"13844","published-online":{"date-parts":[[2026,2,27]]},"container-title":["Contributions to Discrete Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/cdm.ucalgary.ca\/article\/download\/80046\/58851","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/cdm.ucalgary.ca\/article\/download\/80046\/58851","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T07:00:21Z","timestamp":1772607621000},"score":1,"resource":{"primary":{"URL":"https:\/\/cdm.ucalgary.ca\/article\/view\/80046"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,2,27]]}},"URL":"https:\/\/doi.org\/10.55016\/dptxws28","relation":{},"ISSN":["1715-0868"],"issn-type":[{"value":"1715-0868","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,27]]}}}