Strict unimodality of q-polynomials of rooted trees
  We classify rooted trees which have strictly unimodal q-polynomials (plucking polynomial). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients. We discuss which polynomials can be realized as plucking polynomials and whether or not different rooted trees can have the same plucking polynomial. 
Zhiyun Cheng, Sujoy Mukherjee, Jozef H. Przytycki, Xiao Wang, Seung   Yeop Yang
math.CO math.GT