Fubini Polynomials and Generating Series: A Probability Approach

Abstract

This thesis explores fundamental concepts in combinatorial mathematics and probability theory, bridging combinatorial identities and probabilistic interpretations. The first chapter covers foundational elements such as factorials, generating functions, and Stirling numbers. The second chapter introduces probability theory, discussing key distributions and the moment generating function. The final chapter delves into probabilistic versions of degenerate Fubini polynomials, analyzing their properties and recurrence relations. This work aims to deepen the understanding of combinatorial and probabilistic structures, highlighting their theoretical and practical significance.