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Results tagged with co.combinatorics
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user 99278
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
1
vote
Bound of area of intersection
Since the geometry is irrelevant and you are just considering $n$ subsets of equal measure, $I(n,S,k)$ is also the maximum value such that, given any $n$ measure-$S$ subsets of the unit-circumference …
- 399
3
votes
Sum of multinomial coefficients (even distribution)
If you take the averaged sum over all choices of signs $$\frac{1}{2^k}
\sum_{\varepsilon_i = \pm 1} (\varepsilon_1x_1 + \cdots +
\varepsilon_kx_k)^r$$ we see that only the terms with even exponents …
1
vote
Ratio between number of nodes and leaves in a rooted binary tree
We can prove a lower bound on the expression by considering only vertices immediately below a leaf:
$$\frac{[\sum_{v \in T \text{ not a leaf}}2^{h(v)}L(T(v))] + L(T)}{N(T)} \geq \frac{[\sum_{v \text{ …
- 399
3
votes
Accepted
Covering sequences of words
Try $w_0 = b$, $w_1 = bab$, $w_2 = baba^2bab$, $w_3 = baba^2baba^3baba^2bab$, and recursively $w_{i+1} = w_ia^{i+1}w_i$.
Then $\displaystyle \limsup_{i \rightarrow \infty} Pr(w_i,a^n) = \lim_{i \rig …
- 399