Incidence algebra

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In order theory, a field of mathematics, an incidence algebra is an associative algebra,
defined for every locally finite partially ordered set and commutative ring with unity.

Subalgebras called reduced incidence algebras give a natural construction of
various types of generating functions used in combinatorics and number theory.

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An incidence algebra is analogous to a group algebra;
indeed, both the group algebra and the incidence algebra are special cases of a category algebra,
defined analogously; groups and posets being special kinds of categories.