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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.
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
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
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
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