منابع مشابه
Computing the integer partition function
In this paper we discuss efficient algorithms for computing the values of the partition function and implement these algorithms in order to conduct a numerical study of some conjectures related to the partition function. We present the distribution of p(N) for N ≤ 109 for primes up to 103 and small powers of 2 and 3.
متن کاملComputing the partition function for graph homomorphisms
We introduce the partition function of edge-colored graph homomorphisms, of which the usual partition function of graph homomorphisms is a specialization, and present an efficient algorithm to approximate it in a certain domain. Corollaries include efficient algorithms for computing weighted sums approximating the number of k-colorings and the number of independent sets in a graph, as well as a...
متن کاملSome families of identities for the integer partition function
We give a series of recursive identities for the number of partitions with exactly k parts and with constraints on both the minimal difference among the parts and the minimal part. Using these results, we demonstrate that the number of partitions of n is equal to the number of partitions of 2n + d ( n 2 ) of length n, with d-distant parts. We also provide a direct proof for this identity. This ...
متن کاملRestricted integer partition functions
For two sets A and M of positive integers and for a positive integer n, let p(n,A,M) denote the number of partitions of n with parts in A and multiplicities in M , that is, the number of representations of n in the form n = ∑ a∈Amaa where ma ∈M ∪{0} for all a, and all numbers ma but finitely many are 0. It is shown that there are infinite sets A and M so that p(n,A,M) = 1 for every positive int...
متن کاملComputing the Partition Function for Cliques in a Graph
We present a deterministic algorithm which, given a graph G with n vertices and an integer 1 < m ≤ n, computes in nO(lnm) time the sum of weights w(S) over all msubsets S of the set of vertices of G, where w(S) = exp{γmσ(S)+O(1/m)} provided exactly (m 2 ) σ(S) pairs of vertices of S span an edge of G for some 0 ≤ σ(S) ≤ 1, and γ > 0 is an absolute constant. This allows us to tell apart the grap...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2007
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-07-01966-7