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MIT PRIMES/Art of Problem Solving

CROWDMATH 2021: Extremal combinatorics

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Symmetric versions of $u$-free process on sequence
parityhome   0
Jun 8, 2021
I don't mean to add more versions of $Fr$ just for fun. The motivation is to make $Fr$ more symmetric. For example, we know that $Fr(aab, n)$ and $Fr(abb, n)$ are quite different.

One version is $Fb$, where b stands for Bidirectional, and in the process we are allowed to insert a symbol to the beginning of the sequence as long as $u$ is avoided and the required sparsity is still preserved.

Another version is $Fi$, where i stands for Insertion: we can insert any symbol anywhere with the same constraints.

Both these versions can have variant that only respects sparsity, and the process terminates whenever $u$ is present.
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parityhome
Jun 8, 2021
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