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#redirect [[Integer partition#Representations of partitions]] ...

#REDIRECT [[Integer partition#Representations of partitions]] ...

{{about|partitions in the mathematical sense|other uses|Partition (disambiguation)}} ...' is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in [[mathematics]] are ...

...the number of partitions of an integer into parts not divisible by another integer}} ...math> into parts not divisible by <math>d</math> is equal to the number of partitions in which no part is repeated <math>d</math> or more times. This generalizes ...

...tition function (number theory)]], the number of possible partitions of an integer ...

...compositions, but 0 has one composition, the empty sequence. Each positive integer ''n'' has <span style="white-space:nowrap" >2^''n''−1</span> dist ...f a sequence of [[non-negative integer]]s. As a consequence every positive integer admits infinitely many weak compositions (if their length is not bounded). ...

...A001845 : Centered octahedral numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-24}}</ref> * 231 is the number of integer [[partition (number theory)|partitions]] of 16. ...

...770 : Happy numbers|last=|first=|date=|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-27}}</ref> ...ose prime factors are [[Gaussian prime]]s, this means that 133 is a [[Blum integer]]. ...

...ity distribution]] on the set of all [[integer partition|partitions of the integer]] ''n''. Among probabilists and statisticians it is often called the '''mul .... When ''θ''&nbsp;=&nbsp;1, then the distribution is precisely that of the integer partition induced by a uniformly distributed [[random permutation]]. As ''θ ...

There are 124 different polygons of length 12 formed by edges of the [[integer lattice]], counting two polygons as the same only when one is a translated ...A051177|Perfectly partitioned numbers: numbers k that divide the number of partitions p(k)}}</ref> ...

...f>{{OEIS|id=A000567}}</ref> For example, there are <math>x_2=8</math> such partitions for <math>2\cdot 6-5=7</math>, namely ...n integer, then ''x'' is the ''n''-th octagonal number. If ''n'' is not an integer, then ''x'' is not octagonal. ...

...es can be made from three rods with integer lengths of at most 12, and 203 integer squares (not necessarily of unit size) can be found in a staircase-shaped [ ...

** [[Partitions of Poland]] * [[Integer partition]], a way to write an integer as a sum of other integers ...

...case design technique. It is important to consider both valid and invalid partitions when designing test cases. we note that there is a fixed size of [[Integer (computer science)|integer]] hence:- ...

...th>th [[Bell number]] <math>B_n</math>, the number of [[partition of a set|partitions of a set]] of size <math>n</math>, equals ...n]] 1. Sometimes Dobiński's formula is stated as saying that the number of partitions of a set of size <math>n</math> equals the <math>n</math>th moment of that ...

...n such that Mertens' function is zero|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}</ref> 65 is the smallest [[integer]] that can be expressed as a sum of two distinct positive squares in two (o ...

...eorge Andrews of the Pennsylvania State University, the world authority on partitions and ''q''-geometric series}}.</ref> In 1976 he discovered [[Ramanujan]]'s [ ...''The Theory of Partitions'' is the standard reference on the subject of [[integer partition]]s.<ref name="rlc"/> ...

...lored). ''Bottom:'' Of these, there are 4 partitions up to rotation, and 3 partitions up to rotation and reflection.]]{{Short description|Mathematical statement ...ng" is a concise way to say that any two lists of prime factors of a given integer are equivalent with respect to the relation {{mvar|R}} that relates two lis ...

== Relation with partitions == ...nce]] for calculating <math>p(n)</math>, the number of [[integer partition|partitions]] of ''n'': ...

...{{Cite OEIS|sequencenumber= A051894 |name=Number of monic polynomials with integer coefficients of degree n with all roots in unit disc}}</ref> ...ite OEIS|sequencenumber= A000262|name=Number of "sets of lists": number of partitions of {1,..,n} into any number of lists, where a list means an ordered subset} ...