Combinatorial estimates by the switching method
نویسندگان
چکیده
The method of switchings is a standard tool for enumerative and probabilistic applications in combinatorics. In its simplest form, it analyses a relation between two sets to estimate the ratio of their sizes. In a more complicated setting, there is a family of sets connected by some relations. By bounding properties of the relations, bounds can be inferred on the relative sizes of the sets. In this paper we extend the treatment of Fack and McKay (2007) to allow the graph of sets and relations to be an arbitrary directed graph. A special case that frequently occurs in bounding tails of distributions is analysed in detail.
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