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            <title xml:lang="en">An order on circular permutations</title>
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            <idno type="halRefHtml">&lt;i&gt;The Electronic Journal of Combinatorics&lt;/i&gt;, 2021, 28 (3), pp.P3.31. &lt;a target="_blank" href="https://dx.doi.org/10.37236/9982"&gt;&amp;#x27E8;10.37236/9982&amp;#x27E9;&lt;/a&gt;</idno>
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            <idno type="stamp" n="UNIV-TOURS">Université François Rabelais</idno>
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            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
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                <term xml:lang="en">Circular permutations</term>
                <term xml:lang="en">line diagrams</term>
                <term xml:lang="en">Shi vectors</term>
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              <p>Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_n$ (that is, $n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and to an interval in the affine symmetric group $\tilde S_n$ with the weak order. The poset is a semidistributive lattice, and the rank function, whose range is cubic in $n$, is computed by some special formula involving inversions. We prove also some links with Eulerian numbers, triangulations of an $n$-gon, and Young's lattice.</p>
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