What is the relationship between Catalan numbers and number of different ways of partitioning the set of vertices of a convex n-gon into nonintersecting polygons? Catalan numbers sequence describes number of different ways of triangulation of a polygon where the area of the polygon is partitioned into triangles but partitioning the set of vertices of a convex n-gon into nonintersecting polygons is totally irrelevant to that triangulation. As an outcome of my research work I have derived a general formula for the partitioning of the set of vertices and there I used Catalan numbers sequence.
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2$\begingroup$ How is partitioning the set of vertices of a convex $n$-gon different from partitioning any other set of size $n$? I’m sure you have a reasonable question in mind, but you’re really not giving enough detail for most of us to understand what it is. $\endgroup$– Jeremy RickardCommented Mar 27, 2022 at 18:15
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$\begingroup$ Really sorry for not including much important condition, here you have to partition the set of vertices of a convex n-gon into nonintersecting polygons not just polygons. I know there is a direct connection between triangulation of a convex n-gon and Catalan numbers but in this case the partitioning scenario is completely different and really complicated.( I have included that condition to the question) $\endgroup$– Janaka RodrigoCommented Mar 27, 2022 at 23:54
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1$\begingroup$ en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Hipparchus_number $\endgroup$– Sam NeadCommented Mar 28, 2022 at 0:22
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$\begingroup$ Mathstackexchange is a more welcoming forum for elementary questions. Sorry! $\endgroup$– Sam NeadCommented Mar 28, 2022 at 0:23
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$\begingroup$ @ Sam Nead I want to know how to connect partitioning of the area of a convex polygon and partitioning the set of vertices of a convex polygon. It's really hard to see that kind of relationship using the link you have suggested. $\endgroup$– Janaka RodrigoCommented Mar 29, 2022 at 2:48
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