Discrete Structures and Their Interactions
Opis
This text is intended for graduate and upper-level undergraduate students in mathematics who have taken an initial course in discrete mathematics or graph theory. The text introduces a number of discrete structures, such as hypergraphs, finite topologies, preorders, simplicial complexes, and order ideals of monomials, that most graduate students in combinatorics, and even some researchers in the field, seldom experience. The author explains how the discrete structures have important applications in many areas inside and outside of combinatorics. He also shows how to recognize valuable research connections through these structures.