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Combinatorial Route to Algebra: The Art of Composition & Decomposition

Abstract : 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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Pawel Blasiak. Combinatorial Route to Algebra: The Art of Composition & Decomposition. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, 12 (2), pp.381-400. ⟨hal-00994980⟩

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