All Questions
7 questions
2
votes
1
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208
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Proving an exponential sum inequality for symmetric Hamming distance sequences in binary vectors
Background: Let $X = \{0,1\}^k$ represent the set of all binary vectors of length $k$. For two binary vectors $x, y \in X$, the Hamming distance $d_H(x, y)$ is defined as the number of positions where ...
- 349
8
votes
2
answers
484
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Inductive definition of Bernstein polynomials
For $n\in \mathbb{N}$ let $B_n$ be the linear operator taking a function $f$ on the unit interval $I=[0,1]$ to its $n$-th Bernstein polynomial $B_nf$,
$$ B_nf(x):=\sum_{k=0}^n\binom{n}{k} f\Big(\...
- 60.5k
1
vote
1
answer
72
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Independent identical distribution sequence
given a measurable function $\alpha: (\Omega, \mu) \to \mathbb{R}$, and transformation $\sigma : \Omega \to \Omega $.
I found an example such that $\alpha, \alpha\circ \sigma, \alpha\circ \sigma^2, \...
- 553
0
votes
0
answers
119
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the enumeration of 2 dimensional lattice walks with fixed number steps and largest distance from the end point ti the origin
There is actually an one dimensional version of this problem. For each step of the lattice walk, we can move either east for one unit or west for one unit. The problem is that given a fixed $n$ steps ...
- 167
7
votes
5
answers
682
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Bound on sum of complex summands involving binomial coefficients
I am trying to find the asymptotic behavior of the sum:
$$ \sum^n_{i=0} \begin{pmatrix} 2n \\ i \end{pmatrix} x^i y^{2n-i}$$
as $n\rightarrow\infty$. Here $x$, $y$ are complex numbers and I have $|x|...
- 93
1
vote
1
answer
918
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Pros and cons of probability model for permutations
I am studying probability model of random permetuation
Let $b(n; k)$ denote the number of permutations of {1,...,n} with precisely k
inversions ($inv(\pi)$). The analytic approach was considered by L....
0
votes
1
answer
182
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How to Rigorize an inequalities argument
Context
I'm working on a problem involving Lovasz Local Lemma, for proving that there exists a graph with a certain property.
What I need to prove:
There exists some constant $c$, and functions $p,...
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