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Any finite generic set of points on the unit circle corresponds to a permutation in a canonical way. We characterise and enumerate the permutations that arise from this correspondence.

A monotone grid class is a permutation class (i.e., a downset of permutations under the containment order) defined by local mono-tonicity conditions. We give a simplified proof of a result of Mur-phy and Vatter that monotone grid classes of forests are partially well-ordered.

A selection of points drawn from a convex polygon, no two with the same vertical or horizontal coordinate, yields a permutation in a canonical fashion. We characterise and enumerate those permutations which arise in this manner and exhibit some interesting structural properties of the permutation class they form. We conclude with a permutation analogue of… (More)

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