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...

Laguerre–Pólya class Landau–Kolmogorov inequality Multivariate Pólya distribution Pólya's characterization theorem Pólya class Pólya conjecture Polya distribution...

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;...

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

principle Method of distinguished element Pólya enumeration theorem Sieve theory Zeilberger, Doron, Enumerative and Algebraic Combinatorics Björner, Anders...

recurrence theorem (dynamical systems) Poisson limit theorem (probability) Pólya enumeration theorem (combinatorics) Pomeranchuk's theorem (physics) Pompeiu's...

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

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

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...

… , 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...

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

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

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

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...

motivate the creation of classes of combinatorial structures. The Pólya enumeration theorem solves this problem in the unlabelled case. Let f(z) be the ordinary...

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...

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

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...

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

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

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...

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...

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

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

3 (3–4): 375–380, doi:10.1007/BF02579193, MR 0729790, S2CID 13708977. Pólya, George; Tarjan, Robert E.; Woods, Donald R. (October 2009), "Hamiltonian...

consecutive values of a mimic a random variable like a coin flip. Specifically, Pólya and Vinogradov proved (independently) in 1918 that for any nonprincipal...

partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors...

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...