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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

8 votes

Applications of measure, integration and Banach spaces to combinatorics

Fourier Analysis is a major tool in Arithmetic combinatorics (see Tao and Vu's book, they have a chapter named L^p theory, i.e. the theorem of Bourgain's about "long APs in sumsets"). Moreover, one c …
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2 votes

Applications of Representation Theory in Combinatorics

One of the most well known applications of representation theory in combinatorics is the explicit construction of Expander graphs by Margulis (using Kazhdan's property (T)). See any book about expande …