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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 …
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 …