{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T10:19:49Z","timestamp":1648635589033},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"The order ideal $B_{n,2}$ of the Boolean lattice $B_n$ consists of all subsets of size at most $2$. Let $F_{n,2}$ denote the poset refinement of $B_{n,2}$ induced by the rules: $i < j$ implies $\\{i \\} \\prec \\{ j \\}$ and $\\{i,k \\} \\prec \\{j,k\\}$. We give an elementary bijection from the set $\\mathcal{F}_{n,2}$ of linear extensions of $F_{n,2}$ to the set of\u00a0 shifted standard Young tableau of shape $(n, n-1, \\ldots, 1)$, which are counted by the strict-sense ballot numbers. We find a more surprising result when considering the set $\\mathcal{F}_{n,2}^{1}$\u00a0 of minimal poset refinements in which each singleton is comparable with all of the doubletons. We show that $\\mathcal{F}_{n,2}^{1}$ is in bijection with magog triangles, and therefore is equinumerous with alternating sign matrices. We adopt our proof techniques to show that row reversal of an alternating sign matrix corresponds to a natural involution on gog triangles.<\/jats:p>","DOI":"10.37236\/9246","type":"journal-article","created":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T10:11:24Z","timestamp":1613038284000},"source":"Crossref","is-referenced-by-count":0,"title":["De Finetti Lattices and Magog Triangles"],"prefix":"10.37236","volume":"28","author":[{"given":"Andrew","family":"Beveridge","sequence":"first","affiliation":[]},{"given":"Ian","family":"Calaway","sequence":"additional","affiliation":[]},{"given":"Kristin","family":"Heysse","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,2,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p38\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T10:11:25Z","timestamp":1613038285000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i1p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1,14]]}},"URL":"https:\/\/doi.org\/10.37236\/9246","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,12]]}}}