combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that...

the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has...

computer science Integer partition, a way to write an integer as a sum of other integers Multiplicative partition, a way to write an integer as a product...

or an ordered partition of a set, partition of a graph, partition of an integer, partition of an interval, partition of unity, partition of a matrix; see...

where p ( 23 ) = 1255 {\displaystyle p(23)=1255} is the number of integer partitions of 23. Using decimal representation as well, 997 is the 168th and...

number, number of partitions of 38 into nonprime parts 806 = 2 × 13 × 31, sphenic number, nontotient, totient sum for first 51 integers, happy number, Phi(51)...

In the number theory of integer partitions, the numbers p k ( n ) {\displaystyle p_{k}(n)} denote both the number of partitions of n {\displaystyle n}...

." 1234 is the number of integer partitions of 24 without all distinct multiplicities, as well as the number of partitions of 24 into parts that are...

decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater...

negative integer). Here the associated sign is (−1)s with s = m − 1 = −k, therefore the sign is again (−1)k. In summary, it has been shown that partitions into...

science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be partitioned into two...

The 3-partition problem is a strongly NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned...

In number theory, the crank of an integer partition is a certain number associated with the partition. It was first introduced without a definition by...

In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula...

solid partitions are natural generalizations of integer partitions and plane partitions defined by Percy Alexander MacMahon. A solid partition of n {\displaystyle...

sum, while they are considered to define the same integer partition of that number. Every integer has finitely many distinct compositions. Negative numbers...

Erdős–Gallai theorem and the theory of integer partitions. Let m = ∑ d i {\displaystyle m=\sum d_{i}} ; then the sorted integer sequences summing to m {\displaystyle...

inverse pair, and the partition generated via the Lambek–Moser theorem from this pair is just the partition of the positive integers into even and odd numbers...

obtaining asymptotic formulae. Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to...

number of integer partition of 10: the number of ways of expressing 10 as a sum of positive integers. 1111123, one of the forty-two unordered integer partitions...

same. When θ = 1, then the distribution is precisely that of the integer partition induced by a uniformly distributed random permutation. As θ → ∞, the...

American mathematician who specializes in number theory, especially in integer partitions, modular forms, umbral moonshine, the Riemann Hypothesis and the fields...

order. Listing the number of boxes in each row gives a partition λ of a non-negative integer n, the total number of boxes of the diagram. The Young diagram...

natural numbers as the non-negative integers 0, 1, 2, 3, ..., while others define them as the positive integers 1, 2, 3, ... . Some authors acknowledge...

number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and...

sphenic number, number of integer partitions of 20, Smith number 628 = 22 × 157, nontotient, totient sum for first 45 integers 629 = 17 × 37, highly cototient...

integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers...

attribute of an integer partition. A partition of n has a Durfee square of size s if s is the largest number such that the partition contains at least...

order, natural ordering) is a partial order on the set of partitions of a positive integer n that plays an important role in algebraic combinatorics and...

the partition problem, a variant of the knapsack problem from operations research. Some weights are put on a balance scale; each weight is an integer number...