The number of non-crossing perfect plane matchings is minimized (almost) only by point sets in convex position

Andrei Asinowski

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arXiv · 1502.05332

The number of non-crossing perfect plane matchings is minimized (almost) only by point sets in convex position

Andrei Asinowski

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Abstract

It is well-known that the number of non-crossing perfect matchings of $2k$ points in convex position in the plane is $C_k$, the $k$th Catalan number. Garc\'ia, Noy, and Tejel proved in 2000 that for any set of $2k$ points in general position, the number of such matchings is at least $C_k$. We show that the equality holds only for sets of points in convex position, and for one exceptional configuration of $6$ points.

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Andrei Asinowski. 2015-02-18. The number of non-crossing perfect plane matchings is minimized (almost) only by point sets in convex position. https://arxiv.org/abs/1502.05332

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