Non-Koszulness of operads and positivity of Poincar\'e series
  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. 
Vladimir Dotsenko, Martin Markl, and Elisabeth Remm
math.KT math.CO math.CT