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3 unusual facts about Catalan number


28242 Mingantu

The asteroid was named after Minggatu, a Qing era mathematician and astronomer of Mongol ethnicity, who is credited with originally discovering Catalan numbers.

Catalan number

The reflection principle has been widely attributed to Désiré André, but his method did not actually use reflections; and the reflection method is a variation due to Aebly and Mirimanoff.

In 1988, it came to light in an Inner Mongolia University of Technology publication that the Catalan number sequence had been used in China by the Mongolian mathematician Minggantu by 1730.


Combinatorial class

For instance, the triangulations of regular polygons (with size given by the number of sides of the polygon, and a fixed choice of polygon to triangulate for each size) and the set of unrooted binary plane trees (up to graph isomorphism, with a fixed ordering of the leaves, and with size given by the number of leaves) are both counted by the Catalan numbers, so they form isomorphic combinatorial classes.


see also