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arXiv · 2509.14419

On Hilbert series of Koszul operads and a classification result for set-operads

Paul Laubie
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Abstract

Motivated by numerous examples in the literature, we state a conjecture on the Hilbert series of Koszul symmetric operads generated by one element of arity $2$. We prove this conjecture for all Koszul symmetric set-operads generated by one element of arity $2$ by explicitly classifying those. There are $11$ such operads; $4$ of them are new.

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Paul Laubie. 2025-10-27. On Hilbert series of Koszul operads and a classification result for set-operads. https://arxiv.org/abs/2509.14419

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