This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse

New formulas for the multiplicative partition function are developed. Besides giving a fast algorithm for generating these partitions, new identities for additive partitions and the Riemann zeta function are also produced.

The Principle of Indifference was once regarded as a linchpin of probabilistic reasoning, but has now fallen into disrepute as a result of the so-called problem of multiple of partitions. In ‘Evidential symmetry and mushy credence ’ Roger White suggests that we have been too quick to jettison

For a positive integer n, let f(ri) be the number of multiplicative partitions of n. That is, f(n) represents the number of different factorizations of n, where two factorizations are considered the same if they differ only in the order of the factors. For example, /"(12) = 4, since 12 = 6

Let D(s) = P 1 m=1 amm s be the Dirichlet series generated by the innite product

We describe MUSCLE, a new computer program for creating multiple alignments of protein sequences. Elements of the algorithm include fast distance estimation using kmer counting, progressive alignment using a new profile function we call the logexpectation score, and refinement using tree

,0)+2j(mj+1+ · · ·+mk−1), where mj is the number of parts in n (j). This bijection entails an elementary and constructive proof of the Andrews multiple-sum enumerating partitions with frequency conditions. A very natural relation between the k − 1 ordered partitions and restricted paths is also

-valued attribute into multiple intervals. We briefly present theoretical evidence for the appropriateness of this heuristic for use in the binary discretization algorithm used in ID3, C4, CART, and other learning algorithms. The results serve to justify extending the algorithm to derive multiple intervals. We

About a year ago, Herb Wilf[W1] posed, on-line, eight intriguing problems. I don’t know the answer to any of them, but I will say something about the sixth question. Herb Wilf’s 6th Question: Let T (n) be the set of partitions of n for which the (nonzero) multiplicities of its parts are all

For a positive integer n, let f(n) be the number of essentially different ways of writing n as a product of factors greater than 1, where two factorizations of a positive integer are said to be essentially the same if they differ only in the order of the factors. For example, /(12) = 4, since 12 = 2-6-3-4 = 2-2-3. This function was introduced by Hughes and Shallit [1], who proved