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Tuesday, December 8, 2015. Lovász Local Lemma (non-constructive). I read the short (and interesting) presentation. Of the original local Lovász lemma from a lecture by Alistair Sinclair. I report here the proof of this lemma (which was left as an exercise, although a simpler case was proven whose proof contains all the ingredients). 1 Lovász Local Lemma. The proof goes as follows. We first show that for any index $1 le i le n$ and any strict subset $S subset {1, dots,n }$, we have. Mathbb{P} left(A i big...

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dytuxh | dytuxh.blogspot.com Reviews
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Tuesday, December 8, 2015. Lovász Local Lemma (non-constructive). I read the short (and interesting) presentation. Of the original local Lovász lemma from a lecture by Alistair Sinclair. I report here the proof of this lemma (which was left as an exercise, although a simpler case was proven whose proof contains all the ingredients). 1 Lovász Local Lemma. The proof goes as follows. We first show that for any index $1 le i le n$ and any strict subset $S subset {1, dots,n }$, we have. Mathbb{P} left(A i big...
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1 dytuxh
2 pages
3 accueil
4 the lemma states
5 begin{align}
6 end{align}
7 2 other formulations
8 but we have
9 ge frac{1}{e}
10 ge frac{1}{2}
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dytuxh | dytuxh.blogspot.com Reviews

https://dytuxh.blogspot.com

Tuesday, December 8, 2015. Lovász Local Lemma (non-constructive). I read the short (and interesting) presentation. Of the original local Lovász lemma from a lecture by Alistair Sinclair. I report here the proof of this lemma (which was left as an exercise, although a simpler case was proven whose proof contains all the ingredients). 1 Lovász Local Lemma. The proof goes as follows. We first show that for any index $1 le i le n$ and any strict subset $S subset {1, dots,n }$, we have. Mathbb{P} left(A i big...

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dytuxh: Weird binomial identities

http://dytuxh.blogspot.com/2015/12/weird-binomial-identities.html

Tuesday, December 1, 2015. In this post, I present some relatively weird binomial identities. I will start by the symmetric case, and then consider the twisted case. We prove the following identity. C {l,l}(y) underset{def}{=} sum {i=0} l binom{l i}{l} y i = frac{(1 rho) l}{1-y} - frac{y {l 1} {1-y} cdot frac{ rho l}{2} cdot left( 1 frac{1}{ rho} right) {2l 1}. Where $y$ is a formal variable, and $ rho = y/(1-y)$. This identity follows from the classical method of coefficient identification. Frac{(1 rho)...

2

dytuxh: Explicit computations of some direct limits of ordered groups

http://dytuxh.blogspot.com/2015/11/explicit-computations-of-some-direct.html

Friday, November 20, 2015. Explicit computations of some direct limits of ordered groups. The basic definition of direct limits of groups is not so difficult. But concrete computations of these turn out not to be so easy for beginners (like me). I present in this post some computations of this kind. 1 Direct limit - definition and construction. The general definition of direct limit can be found on wikipedia. Here, I will focus on direct limits of partially ordered abelian groups. The partial order is de...

3

dytuxh: November 2014

http://dytuxh.blogspot.com/2014_11_01_archive.html

Friday, November 7, 2014. Funny nonsense about Chaitin $ Omega$ and Riemann $ zeta$. This post will be brief. I don't know anything about Riemann. Zeta$, except the basic definition and the million dollar prize which attracts the most terrible bounty hunters mathematicians. I hardly know more about Chaitin $ Omega$. Yet, I found that they look similar in some sense. Maybe, it's completely obvious, and trivial. Maybe, it's related to something slightly deeper. Anyway, it looks funny. Omega(s {-1}) &= sum ...

4

dytuxh: November 2015

http://dytuxh.blogspot.com/2015_11_01_archive.html

Friday, November 20, 2015. Explicit computations of some direct limits of ordered groups. The basic definition of direct limits of groups is not so difficult. But concrete computations of these turn out not to be so easy for beginners (like me). I present in this post some computations of this kind. 1 Direct limit - definition and construction. The general definition of direct limit can be found on wikipedia. Here, I will focus on direct limits of partially ordered abelian groups. The partial order is de...

5

dytuxh: June 2015

http://dytuxh.blogspot.com/2015_06_01_archive.html

Sunday, June 28, 2015. Ranking function for multiset combinations. Consider a totally ordered finite alphabet $A$. Fix a vector $d = (d s) {s in A}$ of non-negative integers with $n = sum d s$. In this post, I would like to present a somewhat simple ranking function for the set $S(A n,d)$ of vectors $v in A n$ satisfying. D s = text{ number of occurrences of } s text{ in } v. S(A n,d) = binom{n}{(d s) {s in A}. By ranking function, I mean an explicit bijection. 1 Case $ A = 2$. If $v {n-1} = 0$ then it r...

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dytuxh

Tuesday, December 8, 2015. Lovász Local Lemma (non-constructive). I read the short (and interesting) presentation. Of the original local Lovász lemma from a lecture by Alistair Sinclair. I report here the proof of this lemma (which was left as an exercise, although a simpler case was proven whose proof contains all the ingredients). 1 Lovász Local Lemma. The proof goes as follows. We first show that for any index $1 le i le n$ and any strict subset $S subset {1, dots,n }$, we have. Mathbb{P} left(A i big...

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