{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T00:05:34Z","timestamp":1772755534318,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $S \\subseteq \\mathbb{N}$ be a numerical semigroup with multiplicity $m = \\min(S \\setminus \\{0\\})$ and conductor $c=\\max(\\mathbb{N} \\setminus S)+1$. Let $P$ be the set of primitive elements of $S$, and let $L$ be the set of elements of $S$ which are smaller than $c$. A longstanding open question by Wilf in 1978 asks whether the inequality $|P||L| \\ge c$ always holds. Among many partial results, Wilf's conjecture has been shown to hold in case $|P| \\ge m\/2$ by Sammartano in 2012. Using graph theory in an essential way, we extend the verification of Wilf's conjecture to the case $|P| \\ge m\/3$. This case covers more than $99.999\\%$ of numerical semigroups of genus $g \\le 45$.<\/jats:p>","DOI":"10.37236\/9106","type":"journal-article","created":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T03:25:05Z","timestamp":1588821905000},"source":"Crossref","is-referenced-by-count":9,"title":["A Graph-Theoretic Approach to Wilf's Conjecture"],"prefix":"10.37236","volume":"27","author":[{"given":"Shalom","family":"Eliahou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,5,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p15\/8072","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p15\/8072","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T03:25:05Z","timestamp":1588821905000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i2p15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,3]]}},"URL":"https:\/\/doi.org\/10.37236\/9106","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,1]]},"article-number":"P2.15"}}