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.
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 =,
The book was unique at the time because of its arrangement, less by topic and more by method of solution, so arranged in order to build up the student's problem-solving abilities. The preface of the book contains some remarks on general problem solving and mathematical heuristics which anticipate Pólya's later works on that subject ...
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 ...
Can you vary or change your problem to create a new problem (or set of problems) whose solution(s) will help you solve your original problem? Search: Auxiliary Problem: Can you find a subproblem or side problem whose solution will help you solve your problem? Subgoal: Here is a problem related to yours and solved before
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is + = (), =,,, … which gives rise to the sequence,,, … of iterated function applications , (), (()), … which is hoped to converge to a point .
The monodromy theorem gives a sufficient condition for the existence of a direct analytic continuation (i.e., an extension of an analytic function to an analytic function on a bigger set). Suppose D ⊂ C {\displaystyle D\subset \mathbb {C} } is an open set and f an analytic function on D .
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 ...