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3 votes

Conceptual reason why the sign of a permutation is well-defined?

There is an interesting wrong "proof" by Hans Liebeck in the American Mathematical Monthly article Even and odd permutations: He claims that if a product of transpositions $(1\;i)$ is the ...
Peter Mueller's user avatar
1 vote

Maximizing a sum minus its maximal summand

It is true. The proof rests on several observations. The first one is that if you want to maximize $\sum_i i\pi_i$ under the condition $\pi_j\le B_i$ with any prescribed $B_i$, then your best bet is ...
fedja's user avatar
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4 votes

Left-shift cycle generating maps $f:\{0,1\}^{c_0}\to\{0,1\}$ for fixed length $c_0$

Such map cannot exist for $n=c_0+(2^{c_0})!$. Assume the contrary. Write an infinite word by starting with any $c_0$ digits; then, at each step, if the last $c_0$ digits are $x_1,\dots,x_{c_0}$, ...
Ilya Bogdanov's user avatar

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