The identity of three classes of polynomials.
The monotone cumulants
In the present paper we define the notion of generalized cumulants which gives a universal framework for commutative, free, Boolean and especially, monotone probability theories. The uniqueness of generalized cumulants holds for each independence, and hence, generalized cumulants are equal to the usual cumulants in the commutative, free and Boolean cases. The way we define (generalized) cumulants needs neither partition lattices nor generating functions and then will give a new viewpoint to cumulants....
The umbral transfer-matrix method. III: Counting animals.
The umbral transfer-matrix method. IV: Counting self-avoiding polygons and walks.
The umbral transfer-matrix method. V: The Goulden-Jackson cluster method for infinitely many mistakes.