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Encyclopedia of Combinatorial Structures (Introduction)

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This Encyclopedia of Combinatorial Structures (ECS) has originally been written by Stéphanie Petit. The present version is an extended port by Alexis Darrasse and Frédéric Chyzak to the system DynaMoW developed by the latter for the DDMF. The ECS ambitions to be seen as a young cousin of Sloane's Encyclopedia of Integer Sequences with an emphasis on sequences that arise in the context of decomposable combinatorial structures. Like the EIS, it is possible to search the database by the first terms in the sequence, which are then viewed as the sequence of numbers of objects of increasing size in a specified combinatorial structure. It is also possible to search the database by keyword, generating function, or closed form.

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The restriction to sequences arising in this combinatorial framework has for advantage that in many cases a lot of information can be computed automatically. Thus, the result of a successful search is a list of combinatorial structures with, for each of them:

Most of the entries in this list are generated automatically. In some cases, not all the entries could be found by programs and some of them are missing.

This software bases heavily on symbolic libraries by M. Mishna, E. Murray, B. Salvy, and P. Zimmermann. See the links.