Search results
Results from the WOW.Com Content Network
The Pólya enumeration theorem can be used to calculate the number of graphs up to isomorphism with a fixed number of vertices, or the generating function of these graphs according to the number of edges they have. For the latter purpose, we can say that a black or present edge has weight 1, while an absent or white edge has weight 0.
[4]: 23–24 The specific topics treated bear witness to the special interests of Pólya (Descartes' rule of signs, Pólya's enumeration theorem), Szegö (polynomials, trigonometric polynomials, and his own work in orthogonal polynomials) and sometimes both (the zeros of polynomials and analytic functions, complex analysis in general).
Pólya’s theorem can be used to construct an example of two random variables whose characteristic functions coincide over a finite interval but are different elsewhere. Pólya’s theorem. If is a real-valued, even, continuous function which satisfies the conditions =,
Bondy's theorem (graph theory, combinatorics) Bondy–Chvátal theorem (graph theory) Bonnet theorem (differential geometry) Boolean prime ideal theorem (mathematical logic) Borel–Bott–Weil theorem (representation theory) Borel–Carathéodory theorem (complex analysis) Borel–Weil theorem (representation theory) Borel determinacy theorem
According to the De Finetti's theorem, there must be a unique prior distribution such that the joint distribution of observing the sequence is a Bayesian mixture of the Bernoulli probabilities. It can be shown that this prior distribution is a beta distribution with parameters β ( ⋅ ; α , γ ) {\displaystyle \beta \left(\cdot ;\,\alpha ...
Marko Riedel, Pólya's enumeration theorem and the symbolic method; Marko Riedel, Cycle indices of the set / multiset operator and the exponential formula; Harald Fripertinger (1997). "Cycle indices of linear, affine and projective groups". Linear Algebra and Its Applications. 263: 133– 156. doi: 10.1016/S0024-3795(96)00530-7. Harald ...
Pakistan Institute of Nuclear Science & Technology-- Pakistan Mathematical Society-- Pakistan Statistical Society-- Palais–Smale compactness condition-- Palais theorem-- Palatini identity-- Paley construction-- Paley graph-- Paley–Wiener integral-- Paley–Wiener theorem-- Paley–Zygmund inequality-- Palindromic number-- Palindromic prime-- Palm calculus-- Palm–Khintchine theorem-- Pan ...
The graphs were generated using the stick-breaking process view of the Dirichlet process. In probability theory , Dirichlet processes (after the distribution associated with Peter Gustav Lejeune Dirichlet ) are a family of stochastic processes whose realizations are probability distributions .