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Topology and Combinatorics

Combinatorics is a huge subject. It has also been used in algebraic topology as a technical foundation like many other fields. Some of classical topics in topology such as simplcial complex are considerably important in combinatorics. Classical theorems in topology, such as Borsuk-Ulam theorem, proved to be useful in combinatorics and their combinatorial analogues have been obtained. See Introduction in [ JW ] .

Combinatorial tools are also used in algebra, expecially in representation theory . One of the most popular combinatorial objects is quivers . As is written in Introduction of Fiebig’s [ Fie ] , combinatorial objects are useful when we want to relate representation theoretic informations and geometric informations.

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