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arXiv · 1604.08580

Non-Koszulness of operads and positivity of Poincar\'e series

Vladimir Dotsenko·Martin Markl·Elisabeth Remm
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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 the Zeilberger's algorithm for hypergeometric summation to demonstrate that non-Koszulness of that operad cannot be established by hunting for negative coefficients in the inverse of its Poincar\'e series.

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Vladimir Dotsenko, Martin Markl, Elisabeth Remm. 2016-04-28. Non-Koszulness of operads and positivity of Poincar\'e series. https://doi.org/10.25537/dm.2020v25.309-328

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