{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T14:14:37Z","timestamp":1780668877117,"version":"3.54.1"},"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>We prove that the minimal size~$\\mathcal{M}(\\Pi)$ of a maximal matching in the permutahedron $\\Pi$ is asymptotically $n!\/3$. On the one hand, we obtain a lower bound~$\\mathcal{M}(\\Pi) \\ge n! (n-1) \/ (3n-2)$ by considering $4$-cycles in the permutahedron. On the other hand, we obtain an asymptotical upper bound $\\mathcal{M}(\\Pi_n) \\le n!(1\/3+o(1))$ by multiple applications of Hall's theorem (similar to the approach of Forcade for the hypercube) and an exact upper bound~$\\mathcal{M}(\\Pi_n) \\le n!\/3$ by an explicit construction. We also derive bounds on minimum maximal matchings in products of permutahedra.<\/jats:p>","DOI":"10.37236\/14145","type":"journal-article","created":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T13:31:36Z","timestamp":1780666296000},"source":"Crossref","is-referenced-by-count":0,"title":["Minimum Maximal Matchings in Permutahedra"],"prefix":"10.37236","volume":"33","author":[{"given":"Sofia","family":"Brenner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ji\u0159\u00ed","family":"Fink","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hung","family":"Hoang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arturo","family":"Merino","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vincent","family":"Pilaud","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2026,6,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p50\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p50\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T13:31:36Z","timestamp":1780666296000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i2p50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,5]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/14145","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,5]]},"article-number":"P2.50"}}