In this paper we continue the partition explorations made possible by Omega, the computer algebra implementation of MacMahon’s Partition Analysis. The focus of our work has been partitions associated with directed graphs. The graphs considered here are made up of chains of hexagons, and the related generating functions are infinite products. Somewhat unexpectedly, while the generating functions...

The return probabilities of certain random walks on infinite free products of finite groups are shown to obey a Local Limit Theorem of the same type as for nearestneighbor random walks on finite free products. The analysis is based on an infinitedimensional extension of a technique for studying finite algebraic systems of generating functions introduced by the author in [12] and [13].

This paper presents the resolution of sine and cosine as an infinite product from Schlomilch method. It also discusses convergence products sin θ cos θ. Some important Series Infinite Product has been evaluated.

An infinite product IIT= lMi of matrices converges (on the right) if limi __ M, . . . Mi exists. A set Z = (Ai: i > l} of n X n matrices is called an RCP set (rightconvergent product set) if all infinite products with each element drawn from Z converge. Such sets of matrices arise in constructing self-similar objects like von Koch’s snowflake curve, in various interpolation schemes, in construc...