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Results tagged with co.combinatorics
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user 479476
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Partitioning distinguishable objects into indistinguishable blocks
How can you partition n number of distinguishable objects into m number of indistinguishable blocks given that each of the blocks consists of not less than k number of objects.
(k =1 case can be expla …
- 24.2k
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votes
1
answer
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Partitioning the set of vertices of a convex n-gon into nonintersecting polygons
How can you prove that
$$
\sum_{r=0}^{2k-2} (-1)^r \binom{2k-2}{r} (5k-2-r)^{2k-2} =(2k-2)!
$$
This result I have obtained by comparing results of two different approaches for the partitioning of the …
- 3,927
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1
answer
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Combinatorics related plane geometry
There are $n$ men, standing one at each vertex of a convex $n$-gon. If they are allowed to move together along sides or diagonals of the polygon to reach another vertex, how many different ways are th …
- 82.7k
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Different ways of partitioning a convex n -gon [closed]
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 nu …
- 201