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Non-Koszulness of operads and positivity of Poincar\'e series
Preprint
2016-04-28
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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.