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Is there a standard text on the theory of set partitions and/or graph matchings? (I ask both in the same question since it seems feasible that there might be texts containing information on both.)

I don't have any particular question in mind. I'm just interested in finding out the "big results" regarding these two topics, particularly enumerative or structural results.

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up vote 2 down vote accepted

In the 1964 volume of the American Mathematical Monthly there's a paper by Gian-Carlo Rota titled "The Number of Partitions of a Set". See that and the papers it cites. Also check out the Wikipedia articles on Bell numbers and Stirling numbers.

Also look at Richard Stanley's two-volume book Enumerative Combinatorics. A lot of stuff not in there is in stuff he cites.

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In terms of partitions, at least as they pertain to graph theory, Turan's theorem deals with generation of an $r$-partite graph with maximal edges (dubbed the Turan graph). In terms of matchings, Tutte's Theorem is one big result. I've only just finished my introductory Graph Theory course, but those are the two that immediately come to mind.

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I'm really looking more for a text containing much theory, rather than just a few isolated results. I'm hoping to browse them for inspiration. Sorry if this was not clear in my question. – Austin Mohr Apr 20 '12 at 17:57
Gotcha. If I come across any, I'll let you know. Unfortunately, I'm quite new to the field. – JoeDub Apr 20 '12 at 19:20

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