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- Stanley's_reciprocity_theorem abstract "In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone (defined below) and the generating function of the cone's interior.A rational cone is the set of all d-tuples(a1, ..., ad) of nonnegative integers satisfying a system of inequalitieswhere M is a matrix of integers. A d-tuple satisfying the corresponding strict inequalities, i.e., with ">" rather than "≥", is in the interior of the cone.The generating function of such a cone isThe generating function Fint(x1, ..., xd) of the interior of the cone is defined in the same way, but one sums over d-tuples in the interior rather than in the whole cone.It can be shown that these are rational functions. Stanley's reciprocity theorem states thatMatthias Beck, Mike Develin, and Sinai Robins have shown how to prove this by using the calculus of residues. Develin has said that this amounts to proving the result "without doing any work".[citation needed]".
- Stanley's_reciprocity_theorem wikiPageExternalLink 0409562.
- Stanley's_reciprocity_theorem wikiPageID "1093331".
- Stanley's_reciprocity_theorem wikiPageRevisionID "475246076".
- Stanley's_reciprocity_theorem hasPhotoCollection Stanley's_reciprocity_theorem.
- Stanley's_reciprocity_theorem subject Category:Algebraic_combinatorics.
- Stanley's_reciprocity_theorem subject Category:Theorems_in_combinatorics.
- Stanley's_reciprocity_theorem type Abstraction100002137.
- Stanley's_reciprocity_theorem type Communication100033020.
- Stanley's_reciprocity_theorem type Message106598915.
- Stanley's_reciprocity_theorem type Proposition106750804.
- Stanley's_reciprocity_theorem type Statement106722453.
- Stanley's_reciprocity_theorem type Theorem106752293.
- Stanley's_reciprocity_theorem type TheoremsInCombinatorics.
- Stanley's_reciprocity_theorem type TheoremsInDiscreteMathematics.
- Stanley's_reciprocity_theorem comment "In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone (defined below) and the generating function of the cone's interior.A rational cone is the set of all d-tuples(a1, ..., ad) of nonnegative integers satisfying a system of inequalitieswhere M is a matrix of integers.".
- Stanley's_reciprocity_theorem label "Stanley's reciprocity theorem".
- Stanley's_reciprocity_theorem sameAs m.045db3.
- Stanley's_reciprocity_theorem sameAs Q7599389.
- Stanley's_reciprocity_theorem sameAs Q7599389.
- Stanley's_reciprocity_theorem sameAs Stanley's_reciprocity_theorem.
- Stanley's_reciprocity_theorem wasDerivedFrom Stanley's_reciprocity_theorem?oldid=475246076.
- Stanley's_reciprocity_theorem isPrimaryTopicOf Stanley's_reciprocity_theorem.