Non-Koszulness of operads and positivity of Poincaré series

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 Poincaré series.

arXiv comment13 pages. arXiv admin note: text overlap with arXiv:1706.04893