JournalsdmVol. 25pp. 309–328

Non-Koszulness of Operads and Positivity of Poincaré Series

  • Vladimir Dotsenko

    IRMA, UMR 7501, Université de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg Cedex, France

  • Martin Markl

    Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, and MFF UK, Sokolovská 83, 186 75 Prague 8, Czech Republic

  • Elisabeth Remm

    IRIMAS, EA 7499, Université de Haute Alsace, 4, rue des Frères Lumière, 68093 Mulhouse Cedex, France
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Abstract

We prove that the operad of mock partially associative -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 cannot be established by hunting for negative coefficients in the inverse of its Poincaré series.

Cite this article

Vladimir Dotsenko, Martin Markl, Elisabeth Remm, Non-Koszulness of Operads and Positivity of Poincaré Series. Doc. Math. 25 (2020), pp. 309–328

DOI 10.4171/DM/748