Discrete Mathematics & Theoretical Computer Science, Vol 12, No 2 (2010)

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Combinatorial Route to Algebra: The Art of Composition & Decomposition

Pawel Blasiak


We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co-multiplication laws, thereby providing a generic scheme furnishing combinatorial classes with an algebraic structure. The paper is meant as a gentle introduction to the concepts of composition and decomposition with the emphasis on combinatorial origin of the ensuing algebraic constructions.

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