Displaying similar documents to “Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals.”

Antichains in the homomorphism order of graphs

Dwight Duffus, Peter, L. Erdös, Jaroslav Nešetřil, Lajos Soukup (2007)

Commentationes Mathematicae Universitatis Carolinae

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Let 𝔾 and 𝔻 , respectively, denote the partially ordered sets of homomorphism classes of finite undirected and directed graphs, respectively, both ordered by the homomorphism relation. Order theoretic properties of both have been studied extensively, and have interesting connections to familiar graph properties and parameters. In particular, the notion of a duality is closely related to the idea of splitting a maximal antichain. We construct both splitting and non-splitting infinite maximal...

The sum-product algorithm: algebraic independence and computational aspects

Francesco M. Malvestuto (2013)

Kybernetika

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The sum-product algorithm is a well-known procedure for marginalizing an “acyclic” product function whose range is the ground set of a commutative semiring. The algorithm is general enough to include as special cases several classical algorithms developed in information theory and probability theory. We present four results. First, using the sum-product algorithm we show that the variable sets involved in an acyclic factorization satisfy a relation that is a natural generalization of...