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...

sequence 1038 = even integer that is an unordered sum of two primes in exactly n ways 1039 = prime of the form 8n+7, number of partitions of 30 that do not...

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...

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}...

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)...

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...

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...

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...

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

combinatorics, a plane partition is a two-dimensional array of nonnegative integers π i , j {\displaystyle \pi _{i,j}} (with positive integer indices i and j)...

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...

theory and combinatorics, the rank of an integer partition is a certain number associated with the partition. In fact at least two different definitions...

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...

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...

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...

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...

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

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

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

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

The GUID Partition Table (GPT) is a standard for the layout of partition tables of a physical computer storage device, such as a hard disk drive or solid-state...

This is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. OEIS core sequences Index to...

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...

Mertens function returns 0, nontotient, noncototient, number of integer partitions of 20 with an alternating permutation. The HTTP 404 status code is...

congruence patterns in integer partitions Crank of a partition, of a partition of an integer is a certain integer associated with the partition All pages with...

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...