Algebraic and Geometric Methods in Enumerative Combinatorics

摘要: Enumerative combinatorics is about counting. The typical question to find the number of objects with a given set properties. However, enumerative not just In “real life”, when we talk counting, imagine lining up and counting them off: 1, 2, 3, . .. families combinatorial do come us in natural linear order. To give very simple example: count squares an m × n rectangular grid linearly. Instead, use structure understand that ·n. Similarly, more complicated set, usually spend most our efforts understanding underlying individual objects, or itself. Many interest have rich interesting algebraic geometric structure, which often becomes powerful tool towards their enumeration. fact, there are many only know how using these tools. Our goal this chapter highlight some key aspects interplay between algebra, discrete geometry, combinatorics, eye