Application of Burnside?�?s Lemma and Polya?�?s Enumeration Theorem in The Enumeration of Distinct Substituted Naphthalene and Anthracene Compounds

Abstract

In this thesis, we have used Burnside’s lemma and Polya’s Enumeration Theorem. Both Burnside’s lemma and Polya’s Enumeration Theorem are the results of group the ory used to solve counting or enumeration problems. While Burnside’s lemma counts distinct (non-equivalent) objects under symmetry, Polya’s Enumeration Theorem gener alizes this by enumerating all possible configurations, tracking both the unique orbits and the multiplicity of each pattern. One of their most well-known uses is in chemical com binatorics, particularly for the enumeration of chemical isomer(substituted) compounds. So, by using them, we have enumerated the distinct substituted naphthalene compounds through substitution of one or more hydrogen atoms with chlorine (Cl) atoms and the number of distinct substituted anthracene compounds by substituting one or more hydro gen atoms with bromine (Br) atoms.