Title: A semigroup with linearithmic Dehn function

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.