The Pólya enumeration theorem, also known as the Redfield–Pólya theorem and Pólya counting, is a theorem in combinatorics that both follows from and ultimately...

Polya distribution Pólya enumeration theorem Pólya–Vinogradov inequality Pólya inequality Pólya urn model Pólya's theorem Pólya's proof that there is...

Mathematics Pólya Award, awarded by the Mathematical Association of America (MAA) Pólya enumeration theorem Pólya conjecture Hilbert–Pólya conjecture Pólya–Szegő...

scientific discoveries is referred to as Stigler's law of eponymy. Pólya enumeration theorem Cycle index Burnside 1897, §119 Rotman 1995, Chapter 3 Cull, Paul;...

able to enumerate filled slot configurations using either Pólya enumeration theorem in the unlabelled case or the labelled enumeration theorem in the labelled...

problems tend to be easier. As with combinatorial enumeration more generally, the Pólya enumeration theorem is an important tool for reducing unlabeled problems...

combinatorial mathematics, the labelled enumeration theorem is the counterpart of the Pólya enumeration theorem for the labelled case, where we have a...

count these orbits, and thus necklaces and bracelets, using Pólya's enumeration theorem. There are N k ( n ) = 1 n ∑ d ∣ n φ ( d ) k n / d = 1 n ∑ i...

element Pólya enumeration theorem Sieve theory (sequence A003763 in the OEIS) (sequence A209077 in the OEIS) Zeilberger, Doron, Enumerative and Algebraic...

himself written, its original proof was by Jörg Siebeck in 1864. Pólya enumeration theorem. This was proven in 1927 in a difficult paper by J. H. Redfield...

(algebra) Perfect graph theorem (graph theory) Perlis theorem (graph theory) Planar separator theorem (graph theory) Pólya enumeration theorem (combinatorics)...

treated bear witness to the special interests of Pólya (Descartes' rule of signs, Pólya's enumeration theorem), Szegö (polynomials, trigonometric polynomials...

book From Polychords to Pólya: Adventures in Musical Combinatorics is about the application of the Pólya enumeration theorem to the counting and classification...

group, one can enumerate equivalence classes due to the group's action. This is the main ingredient in the Pólya enumeration theorem. Performing formal...

can be counted using Burnside's lemma or its generalization, Pólya enumeration theorem. Consider the seven Tetris pieces (I, J, L, O, S, T, Z), known...

of electron transfer under action of light Pólya enumeration theorem, a mathematical theorem in enumerative combinatorics Potential evapotranspiration...

are connected with the use of the Pólya enumeration theorem in combinatorial groups and combinatorial enumerations. There is a formula for calculating...

what is now called Pólya enumeration theorem (PET) in 1927, ten years ahead of similar but independent discovery made by George Pólya. Redfield was a great-grandson...

… , n q {\displaystyle n_{1},\dotsc ,n_{q}} in the sense of Pólya enumeration theorem. Particular cases include the simple computation E ⁡ [ ∏ i = 1...

is symmetric under a diagonal reflection of the board. Via the Pólya enumeration theorem, these numbers form one of the key components of a formula for...

2.3. Generating inequivalent patterns (includes discussion of Pólya enumeration theorem) (see "Techniques for Isomorph Rejection", chapter 4 of "Classification...

calculated by plugging the numbers of cycle structures into the Pólya enumeration theorem. This number of colorings is n 7 + 21 n 5 + 98 n 3 + 48 n 168...

The techniques he used mainly concern the enumeration of graphs with particular properties. Enumerative graph theory then arose from the results of...

Combinatorics, 1996, pp. 421–426. B. Shapiro, J. Borcea, P. Brändén, "Pólya-Schur master theorems for circular domains and their boundaries", Annals of Mathematics...

The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic...

George Pólya, based on the evidence, that most numbers less than any particular limit have an odd number of prime factors. However, this Pólya conjecture...

Mathematics: A Basic Guide, John Wiley & Sons, p. 181, ISBN 9780471461630. Pólya, George; Tarjan, Robert E.; Woods, Donald R. (2009), Notes on Introductory...

structures. Matroid Greedoid Ramsey theory Van der Waerden's theorem Hales–Jewett theorem Umbral calculus, binomial type polynomial sequences Combinatorial...

of analytic number theory, but his name has become known for the Hilbert–Pólya conjecture, for reasons that are anecdotal. Ernst Hellinger, a student of...

the adjacency matrix), and one may use counting theorems (e.g., Pólya enumeration theorem) to enumerate all edge sets (linkages between polyhedra) that...