{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:13Z","timestamp":1753893793373,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $I_n$ be the ideal of all algebraic relations on the slopes of the ${n\\choose2}$ lines formed by placing $n$ points in a plane and connecting each pair of points with a line.  Under each of two natural term orders, the ideal of $I_n$ is generated by monomials corresponding to permutations satisfying a certain pattern-avoidance condition.  We show bijectively that these permutations are enumerated by the updown (or Euler) numbers, thereby obtaining a formula for the number of generators of the initial ideal of $I_n$ in each degree.<\/jats:p>","DOI":"10.37236\/171","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:28:34Z","timestamp":1578698914000},"source":"Crossref","is-referenced-by-count":1,"title":["Updown Numbers and the Initial Monomials of the Slope Variety"],"prefix":"10.37236","volume":"16","author":[{"given":"Jeremy L.","family":"Martin","sequence":"first","affiliation":[]},{"given":"Jennifer D.","family":"Wagner","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,7,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r82\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r82\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T21:50:37Z","timestamp":1579297837000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/171","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,7,9]]},"article-number":"R82"}}