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            <title xml:lang="en">Enumerating Triangulations of Convex Polytopes</title>
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            <idno type="halRefHtml">&lt;i&gt;Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001&lt;/i&gt;, 2001, Paris, France. pp.111-122, &lt;a target="_blank" href="https://dx.doi.org/10.46298/dmtcs.2295"&gt;&amp;#x27E8;10.46298/dmtcs.2295&amp;#x27E9;&lt;/a&gt;</idno>
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                  <title>Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001</title>
                  <date type="start">2001</date>
                  <settlement>Paris</settlement>
                  <country key="FR">France</country>
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                <editor>Cori</editor>
                <editor>Robert and Mazoyer</editor>
                <editor>Jacques and Morvan</editor>
                <editor>Michel and Mosseri</editor>
                <editor>Rémy</editor>
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                <term xml:lang="en">enumeration</term>
                <term xml:lang="en">triangulation</term>
                <term xml:lang="en">bistellar flip</term>
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              <p>A triangulation of a finite point set A in $\mathbb{R}^d$ is a geometric simplicial complex which covers the convex hull of $A$ and whose vertices are points of $A$. We study the graph of triangulations whose vertices represent the triangulations and whose edges represent geometric bistellar flips. The main result of this paper is that the graph of triangulations in three dimensions is connected when the points of $A$ are in convex position. We introduce a tree of triangulations and present an algorithm for enumerating triangulations in $O(log log n)$ time per triangulation.</p>
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