ARITHMETIC PRODUCT ON COMBINATORIAL SPECIES

• Main Author: REZA GUMAY (NIM: 10114092), FARHAN
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/27171
• Institution: Institut Teknologi Bandung

This undergraduate thesis will discuss about combinatorial species and their applications in various fields in mathematics. Initially, there will be an introduction about the definition of combinatorial species, examples of combinatorial species, some basic operations of combinatorial species, and using combinatorial species as enumerative tool to enumerate combinatorial object. <br /> <br /> <br /> Next, the discussion will focus on new operation called arithmetic product. The arithmetic product gives combinatorial meaning to the Dirichlet series and to the Lambert Series in the context of species. In addition, arithmetic product will give a notion of multiplicative species, which is an analogy in the field of combinatorics of previously known multiplicative function. Arithmetic product will also be used to proof the cyclotomic identity. Last, will be shown how arithmetic product can be used to proof the cyclotomic identity. <br />