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Results tagged with co.combinatorics
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user 7092
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
42
votes
Collecting alternative proofs for the oddity of Catalan
Taking the fact that Catalan numbers $C_n$ measure the number of binary trees on $n$ nodes, we can find an involution on the set of these trees: choose the lexicographically first node in the tree tha …
- 1,951
4
votes
Important formulas in combinatorics
This is a little bit of a lark, but I would argue it still marks important progress in combinatorics: $T=1+T^2\implies T^7=T$. Specifically, this is the (loose) initial justification for the "Seven Tr …
3
votes
Mathematics of the 24 game
To expand on Kevin's comment (and using an answer since a comment doesn't have enough characters!) : one other obvious-but-relevant constraint that's going to be an issue for large values of $N$ is th …
- 1,951
1
vote
Indexing schemes of binary sequences
You want Volume 4, Fascicle 3 of Knuth's The Art of Computer Programming, chapter 7.2.1.3: "Generating All Combinations" - I won't include links because everyone has a favorite online bookseller, but …
- 1,951
1
vote
Geometric probabilistic problem on triangles on a plane
A bit too long for a comment, here's one suggestion: take $a\lt b\lt c$ and use $(0,0)$ and $(c,0)$ as two points of the triangle. The third point $(x,y)$ (taking $y\gt 0$ WLOG) can be found in whatev …
- 1,951