On Mappings on the Hypercube with Small Average Stretch

Lucas Boczkowski
Lucas Boczkowski

arXiv: Combinatorics, 2019.

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Abstract:

Let $A \subseteq \{0,1\}^n$ be a set of size $2^{n-1}$, and let $\phi \colon \{0,1\}^{n-1} \to A$ be a bijection. We define the average stretch of $\phi$ as ${\sf avgStretch}(\phi) = {\mathbb E}[{\sf dist}(\phi(x),\phi(x'))]$, where the expectation is taken over uniformly random $x,x' \in \{0,1\}^{n-1}$ that differ in exactly one coordi...More

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