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Results tagged with co.combinatorics
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user 428
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
28
votes
Accepted
Singmaster's conjecture
There is an upper bound of $O\left(\frac{(\log n)(\log \log \log n)}{(\log \log n)^3}\right)$ due to Daniel Kane: see "Improved bounds on the number of ways of expressing t as a binomial coefficient, …
- 6,589
15
votes
A random walk matrix has eigenvalue 1 with multiplicty 1 - why?
For large enough n, the matrix B = A + A2 + ... + An has positive entries since there's a path of length at most n connecting any two vertices. Thus by the Perron-Frobenius theorem B has a unique max …
- 6,589
12
votes
Accepted
Knot groups with big number of generators
If $\pi_1(S^3\setminus K)$ has a presentation with $n$ generators then its representation variety $\mathrm{Hom}(\pi_1(S^3\setminus K),SL_2(\mathbb{C}))$ is a subvariety of $(SL_2(\mathbb{C}))^n$, whic …
- 6,589