On the modes of the Poisson distribution of order k
  Sharp upper and lower bounds are established for the modes of the Poisson distribution of order k. The lower bound established in this paper is better than the previously established lower bound. In addition, for k = 2, 3, 4, 5, a recent conjecture is presently proved solving partially an open problem since 1983. 
Constantinos Georghiou, Andreas N. Philippou, Abolfazl Saghafi
math.ST stat.TH