Date of Award
Master of Science
Emil D. Schwab
In the mid 1960's, the incidence algebra was introduced in the seminal paper of Gian-Carlo Rota. He addressed the importance of the Mobius function in combinatorics. In particular, the incidence algebra of a locally finite poset plays an essentially unifying role in the theory of the Mobius function. One of the significant generalizations is the incidence algebra of a Mobius category introduced by Pierre Leroux. With the help from Mobius category, it was exciting to be able to extend the combinatorial results more broadly than just on posets. Before attempting to study this generalization of the Mobius function, we have to begin with the basic concepts needed to define the incidence algebra. In the first chapter, we will see some basic concepts and illustrations of incidence functions in posets. In the second chapter, we will introduce the decomposition-finite category C , the incidence algebra of C , and the Mobius function of the Mobius category C .
Received from ProQuest
Liao, Yiyu, "Incidence Functions" (2010). Open Access Theses & Dissertations. 2716.