Non-Koszulness of operads and positivity of Poincaré series

Dotsenko, Vladimir; Markl, Martin; Remm, Elisabeth

doi:10.25537/dm.2020v25.309-328

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Non-Koszulness of operads and positivity of Poincaré series

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Dotsenko, Vladimir
Max Planck Institute for Mathematics, Max Planck Society;

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Markl, Martin
Max Planck Institute for Mathematics, Max Planck Society;

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Remm, Elisabeth
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Dotsenko, V., Markl, M., & Remm, E. (2020). Non-Koszulness of operads and positivity of Poincaré series. Documenta Mathematica, 25, 309-328. doi:10.25537/dm.2020v25.309-328.

Cite as: https://hdl.handle.net/21.11116/0000-0006-9577-C

Abstract

We prove that the operad of mock partially associative $n$-ary algebras is not Koszul, as conjectured by the second and the third author in 2009, and utilise Zeilberger’s algorithm for hypergeometric summation to demonstrate that non-Koszulness of that operad for n = 8 cannot be established by hunting for negative coeﬃcients in the inverse of its Poincaré series.