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cameroncounts.wordpress.com | ||
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gilkalai.wordpress.com
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| | | | | Frankl's conjecture Frankl's conjecture is the following: Let $latex \cal A$ be a finite family of finite subsets of $latex N=\{1,2,\dots,n\}$ which is closed under union, namely, if $latex S,T \in {\cal A}$ thenalso $latex S \cup T \in {\cal A}$. Then there exists an element $latex x$ which belongs to at least half the... | |
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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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mikespivey.wordpress.com
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| | | | | The Riemann zeta function $latex \zeta(s)$ can be expressed as $latex \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}$, for complex numbers s whose real part is greater than 1. By analytic continuation, $latex \zeta(s)$ can be extended to all complex numbers except where $latex s = 1$. The power sum $latex S_a(M)$ is given by $latex S_a(M) =... | |
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nambulous.wordpress.com
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| | | https://youtu.be/lA4z4lQGmdc | ||
