منابع مشابه
Restricted partitions
We prove a known partitions theorem by Bell in an elementary and constructive way. Our proof yields a simple recursive method to compute the corresponding Sylvester polynomials for the partition. The previous known methods to obtain these polynomials are in general not elementary. 1. Proof of Bell's theorem. The main purpose of this section is to prove the following theorem, originally proved b...
متن کاملRestricted Partitions Elementary Methods
In [1] certain restricted partitions were studied in an elementary way. In this article we study other problem about restricted partitions. We prove the following theorem in a direct way and using elementary methods ( combinatory and mathematical induction). Theorem 1. Let n be a positive integer, and let A1, A2, . . . , An be n positive integers. Then, for all positive integers N = MK + r, the...
متن کاملWeighted paths between partitions
Developing from a concern in bioinformatics, this paper analyses alternative metrics between partitions. From both theoretical and applicative perspectives, a seemingly most appropriate distance between any two partitions is HD, which counts the number of atoms finer than either one but not both. While faithfully reproducing the traditional Hamming distance between subsets, HD is very sensible ...
متن کاملEfficient Computation of Restricted Partitions
Have you ever wondered how many ways the total of 5 dollars can be made with coins having cent values {1, 2, 5, 10, 20, 50, 100, 200}? Would you like to take a guess at how many ways there are? Would you be surprised if I told you there were 6295434? Maybe we should tone it down a bit and ask how many ways there are to make 50 cents. There are still 451! Lets step back once more and determine h...
متن کاملRandom partitions with restricted part sizes
For a subsetS of positive integers let (n,S)be the set of partitions ofn into summands that are elements of S. For every λ ∈ (n,S), let Mn(λ) be the number of parts, with multiplicity, that λ has. Put a uniform probability distribution on (n,S), and regardMn as a random variable. In this paper the limiting density of the (suitably normalized) random variableMn is determined for sets that are su...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1959
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-5-4-371-380