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...

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)...

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 40 ways 1039 = prime of the form 8n+7, number of partitions of 30 that do not...

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...

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}...

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...

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...

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...

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

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

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...

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

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...

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...

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...

× 7 × 11, sphenic number, square pyramidal number, the number of integer partitions of 18. 385 = 102 + 92 + 82 + 72 + 62 + 52 + 42 + 32 + 22 + 12 386...

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

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

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...

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...

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 statistical mechanics concept Partition function (number theory), the number of possible partitions of an integer This disambiguation page lists articles...

In mathematics, Young's lattice is a lattice that is formed by all integer partitions. It is named after Alfred Young, who, in a series of papers On quantitative...

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...