A note on how the problem of Partion of Integers show in Caching

In this article, we show how the finding the number of partitions of same size of a positive integer show up in caching networks. We present a stochastic model for caching where user requests (represented with positive integers) are a random process with uniform distribution and the sum of user requests plays an important role to tell us about the nature of the caching process. We discuss Euler's generating function to compute the number of partitions of a positive integer of same size. Also, we derive a simple approximation for guessing the guessing the number of partitions of same size and discuss some special sequences. Lastly, we present a simple algorithm to enumerate all the partitions of a positive integer of same size.