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Results tagged with co.combinatorics
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user 169474
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
2
votes
upper bound on sum of product of binomial coefficients
I agree with your formula. You choose $j \in \{0,\ldots,m-\ell\}$ (it will be the cardinal of $A \cap Y$, and given such a $j$ you choose independently $j$ elements in $Y$ and $m-j$ elements in $X$.
H …
- 3,808
1
vote
Computation involving Gauss integer function
For every real number $x$ and every positive integer $m$, one has
$$\sum_{a=0}^{m-1} \Big\lfloor x+\frac{a}{m} \Big\rfloor = \lfloor mx \rfloor.$$
To prove this, note that $x$ belongs to the interval …
- 3,808
2
votes
Accepted
Is equal natural density on intervals with matching areas but opposite signs sufficient to u...
Let us take the $\theta_n$ in the interval $[0,2\pi)$.
For every $N \ge 1$, set
$$\mu_N = \frac1N\sum_{n=1}^N\delta_{\theta_n} \text{ and } \nu_N := \mathbb{1}_{(0,\pi)\cup(\pi,2\pi)}\mu_N.$$
The exis …
- 3,808