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In either case, the partition function may be solved exactly using eigenanalysis. If the matrices are all the same matrix W , the partition function may be approximated as the N th power of the largest eigenvalue of W , since the trace is the sum of the eigenvalues and the eigenvalues of the product of two diagonal matrices equals the product ...
In computer science, pseudopolynomial time number partitioning is a pseudopolynomial time algorithm for solving the partition problem.. The problem can be solved using dynamic programming when the size of the set and the size of the sum of the integers in the set are not too big to render the storage requirements infeasible.
The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and particles with the environment, at fixed temperature, volume, and chemical potential. Other types of partition functions can be defined for different circumstances; see partition function (mathematics) for
The partition problem is a special case of two related problems: In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S).
These three objective functions are equivalent when k=2, but they are all different when k≥3. [6] [7] All these problems are NP-hard, [8] but there are various algorithms that solve it efficiently in many cases. Some closely-related problems are: The partition problem - a special case of multiway number partitioning in which the number of ...
An example is the partition problem. Both weak NP-hardness and weak polynomial-time correspond to encoding the input agents in binary coding. If a problem is strongly NP-hard, then it does not even have a pseudo-polynomial time algorithm. It also does not have a fully-polynomial time approximation scheme. An example is the 3-partition problem.
A partition in which no part occurs more than once is called strict, or is said to be a partition into distinct parts. The function q(n) gives the number of these strict partitions of the given sum n. For example, q(3) = 2 because the partitions 3 and 1 + 2 are strict, while the third partition 1 + 1 + 1 of 3 has repeated parts.
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution.