The structure of the ring of Hodge cycles on a certain family of abelian varieties of CM-type is investigated. This leads to an interesting combinatorial problem related to posets based on complete -ary trees. A complete solution to the problem is given for the case .
"Hodge cycles on abelian varieties associated to the complete binary trees." J. Math. Soc. Japan 58 (1) 55 - 82, JANUARY, 2006. https://doi.org/10.2969/jmsj/1145287093