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arXiv · 2311.17835

A semigroup with linearithmic Dehn function

Roman Repeev
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Abstract

It is known that there is no finitely presented group for which the Dehn function lies asymptotically strictly between linear and quadratic functions. This work presents an example of a semigroup that has Dehn function equivalent to $n \log n$, thus it lies strictly inside the said gap. The example is obtained by symmetrizing the rewriting rules of a particular semi-Thue system, which has the derivational complexity function $n \log n$. We also show that such connection is not universal by providing a semi-Thue system, for which the Dehn function of the symmetrized semigroup asymptotically differs from the derivational complexity of the initial system.

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Roman Repeev. 2023-11-29. A semigroup with linearithmic Dehn function. https://arxiv.org/abs/2311.17835

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