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Results tagged with co.combinatorics
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user 90066
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
2
votes
1
answer
128
views
Independent decomposition of coordinate distribution
Let $\mathbf{x}$ be a random Gaussian vector in $\mathbb{R}^n$, i.e. $\mathbf{x}\sim\mathcal{N}(\mathbf{0},\mathbf{I}_n)$. Then for any fixed unit vector $\mathbf{u}$, one has $\mathbf{u}\mathbf{u}^\t …
- 515
2
votes
1
answer
196
views
Guess (or upper bound) the general formula for a double sequence
Let $t,s \geq 0$ be integers. We have the following recursive formula:
$$f(t+1,s) = f(t,s) + f(t,s-1) + \sum_{0\leq a,b,c \leq h(t):\\a+b+c = s-1}f(t,a)f(t,b)f(t,c),$$ where
$$h(t) = \frac{1}{2}3^t -\ …
- 515
1
vote
0
answers
86
views
Lower bound the ratio of the combinatorial quantities
Suppose $p < q$, $s = p^{d}$ for some fixed $d \in (0,1)$, let $p$ goes to infinity, define the following quantity,
\begin{aligned}
\quad f(j) = \sum_{i = 0}^{\min(j,s)}{s \choose i}{p-s \choose i}{s …
- 515