Petal projection

<p>In <a href="/facts/Knot_theory/mb7rtqVP">knot theory</a>, a petal projection of a knot is a <a href="/facts/Knot_diagram/mb7rtqVP">knot diagram</a> with a single crossing, at which an odd number of non-nested arcs ("petals") all meet. Because the above-below relation between the branches of a knot at this crossing point is not apparent from the appearance of the diagram, it must be specified separately, as a <a href="/facts/Permutation/JSw9ukmv">permutation</a> describing the top-to-bottom ordering of the branches.
</p><p>Every knot or link has a petal projection; the minimum number of petals in such a projection defines a <a href="/facts/Knot_invariant/BEvEEpHQ">knot invariant</a>, the petal number of the knot. Petal projections can be used to define the Petaluma model, a family of <a href="/facts/Probability_distribution/EpsKKVRu">probability distributions</a> on knots with a given number of petals, defined by choosing a <a href="/facts/Random_permutation/zJMPNXlz">random permutation</a> for the branches of a petal diagram.
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Petal projection open-in-new

Petal projection