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...
29 KB (3,388 words) - 00:44, 18 June 2024
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...
27 KB (4,364 words) - 22:48, 7 August 2024
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...
2 KB (320 words) - 17:15, 24 July 2024
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...
4 KB (237 words) - 00:57, 26 February 2024
1000 (number) (category Integers)
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...
158 KB (25,900 words) - 13:44, 15 August 2024
800 (number) (category Integers)
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)...
22 KB (3,851 words) - 14:22, 14 August 2024
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...
25 KB (2,981 words) - 18:28, 21 June 2024
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}...
3 KB (467 words) - 17:44, 25 February 2024
Pentagonal number theorem (redirect from Euler's partition theorem)
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...
14 KB (2,114 words) - 17:17, 2 July 2024
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...
19 KB (2,441 words) - 17:19, 5 August 2024
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...
15 KB (2,260 words) - 11:29, 14 July 2024
solid partitions are natural generalizations of integer partitions and plane partitions defined by Percy Alexander MacMahon. A solid partition of n {\displaystyle...
7 KB (1,322 words) - 00:02, 25 February 2024
Composition (combinatorics) (category Integer partitions)
sum, while they are considered to define the same integer partition of that number. Every integer has finitely many distinct compositions. Negative numbers...
6 KB (914 words) - 13:26, 11 May 2024
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...
12 KB (1,276 words) - 16:00, 29 May 2024
Ken Ono (section Integer partitions)
American mathematician who specializes in number theory, especially in integer partitions, modular forms, umbral moonshine, the Riemann Hypothesis and the fields...
21 KB (1,805 words) - 16:52, 6 August 2024
Combinatorics (section Partition theory)
obtaining asymptotic formulae. Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to...
32 KB (3,441 words) - 08:19, 6 August 2024
same. When θ = 1, then the distribution is precisely that of the integer partition induced by a uniformly distributed random permutation. As θ → ∞, the...
4 KB (532 words) - 21:35, 24 February 2024
42 (number) (category Integers)
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...
61 KB (7,564 words) - 15:22, 13 August 2024
Young tableau (category Integer partitions)
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...
22 KB (2,871 words) - 00:59, 26 February 2024
number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and...
35 KB (4,795 words) - 03:23, 20 December 2023
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...
9 KB (1,248 words) - 18:35, 3 March 2024
600 (number) (category Integers)
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...
23 KB (3,909 words) - 19:07, 11 August 2024
400 (number) (category Integers)
Mertens function returns 0, nontotient, noncototient, number of integer partitions of 20 with an alternating permutation. HTTP status code for "Not Found"...
36 KB (5,422 words) - 17:19, 16 August 2024
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...
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integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers...
30 KB (4,205 words) - 03:35, 29 July 2024
Birthday problem (section Partition problem)
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...
51 KB (6,844 words) - 09:56, 18 July 2024
parametrized by a positive integer k, and called k-way number partitioning. The input to the problem is a multiset S of numbers (usually integers), whose sum is k*T...
32 KB (4,754 words) - 00:54, 26 January 2024
refinement of a tagged partition x0, …, xn together with t0, …, tn − 1 if for each integer i with 0 ≤ i ≤ n, there is an integer r(i) such that xi = yr(i)...
6 KB (561 words) - 10:32, 11 December 2023
theory and combinatorics, the rank of an integer partition is a certain number associated with the partition. In fact at least two different definitions...
12 KB (1,361 words) - 19:04, 1 March 2024
Rogers–Ramanujan identities (category Integer partitions)
identities are two identities related to basic hypergeometric series and integer partitions. The identities were first discovered and proved by Leonard James...
39 KB (5,920 words) - 06:26, 10 May 2024