Geodesic
Non-Koszulness of Operads and Positivity of Poincaré Series
Documenta mathematica, Tome 25 (2020), pp. 309-328.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 for $n=8$ cannot be established by hunting for negative coefficients in the inverse of its Poincaré series.
Classification : 18M70, 13D40, 33E30, 33F10, 39A06, 39A22
Keywords: operad, Koszul duality, Koszulness, Zeilberger's algorithm 
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     author = {Dotsenko, Vladimir and Markl, Martin and Remm, Elisabeth},
     title = {Non-Koszulness of {Operads} and {Positivity} of {Poincar\'e} {Series}},
     journal = {Documenta mathematica},
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Dotsenko, Vladimir; Markl, Martin; Remm, Elisabeth. Non-Koszulness of Operads and Positivity of Poincaré Series. Documenta mathematica, Tome 25 (2020), pp. 309-328. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a59/