In this paper, we derive some new symmetric properties of 𝑘-Fibonacci numbers by making use of symmetrizing operator. We also give some new generating functions for the products of some special ...

This is a preview. Log in through your library . Abstract Gontcharov obtained the joint probability generating function for the numbers of runs of all lengths, both of successes and failures, in a ...

Partition functions, which enumerate the distinct ways a positive integer may be expressed as a sum of positive integers, have long captivated mathematicians due to their deep connections with number ...