ON FINDING COEFFICIENT OF GENERATING FUNCTION

William W.S. Chen

William W.S. Chen Department of Statistics, The George Washington University, Washington D.C. 20013, USA

Keywords: A sum of 25 when 10 dice are rolled, Generating functions, Inclusion exclusion events study, Polya's enumeration formula, Recurrence relation, Selection and arrangement problems, Two equal unordered piles.

Abstract

This paper review the method of determining the coefficients of a generating function. Generating functions are a convenient tool for handling special constraints in selection and arrangement problems. It can be used in recurrence relations, inclusion exclusion events study, and polya’s enumeration formula. It may also help to solve some other combinatorial problems. Generating functions are a kind of abstract problem-solving technique once we understand it may easy to model a broad spectrum of combinatorial problems. In this paper, we will use
some vivid examples to demonstrate both the theoretical and applicable results of generating function.

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