{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:20:32Z","timestamp":1759335632303,"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>Ascent sequences were introduced by Bousquet-M\u00e9lou, Claesson, Dukes and Kitaev in their study of $(\\bf{2+2})$-free posets. An ascent sequence of length $n$ is a nonnegative integer sequence $x=x_{1}x_{2}\\ldots x_{n}$ such that $x_{1}=0$ and $x_{i}\\leq {\\rm asc}(x_{1}x_{2}\\ldots x_{i-1})+1$ for all $1&lt;i\\leq n$, where ${\\rm asc}(x_{1}x_{2}\\ldots x_{i-1})$ is the number of ascents in the sequence $x_{1}x_{2}\\ldots x_{i-1}$. We let $\\mathcal{A}_n$ stand for the set of such sequences and use $\\mathcal{A}_n(p)$ for the subset of sequences avoiding a pattern $p$. Similarly, we let $S_{n}(\\tau)$ be the set of $\\tau$-avoiding permutations in the symmetric group $S_{n}$. Duncan and Steingr\u00edmsson have shown that the ascent statistic has the same distribution over\u00a0 $\\mathcal{A}_n(021)$ as over $S_n(132)$. Furthermore, they conjectured that the pair $({\\rm asc}, {\\rm rmin})$ is equidistributed over $\\mathcal{A}_n(021)$ and\u00a0 $S_n(132)$ where ${\\rm rmin}$ is the right-to-left minima statistic.\u00a0 We prove this conjecture by constructing a bistatistic-preserving bijection.<\/jats:p>","DOI":"10.37236\/2472","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:56:29Z","timestamp":1578711389000},"source":"Crossref","is-referenced-by-count":5,"title":["On 021-Avoiding Ascent Sequences"],"prefix":"10.37236","volume":"20","author":[{"given":"William Y.C.","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alvin Y.L.","family":"Dai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Theodore","family":"Dokos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tim","family":"Dwyer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruce E.","family":"Sagan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p76\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p76\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:23:29Z","timestamp":1579260209000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p76"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2472","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,3,31]]},"article-number":"P76"}}