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restricted integer partitions

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1: 26.9 Integer Partitions: Restricted Number and Part Size
§26.9(i) Definitions
Table 26.9.1: Partitions p k ( n ) .
n k
Figure 26.9.1: Ferrers graph of the partition 7 + 4 + 3 + 3 + 2 + 1 .
§26.9(ii) Generating Functions
§26.9(iii) Recurrence Relations
2: 26.10 Integer Partitions: Other Restrictions
§26.10(i) Definitions
Table 26.10.1: Partitions restricted by difference conditions, or equivalently with parts from A j , k .
p ( 𝒟 , n ) p ( 𝒟 2 , n ) p ( 𝒟 2 , T , n ) p ( 𝒟 3 , n )
§26.10(ii) Generating Functions
§26.10(iii) Recurrence Relations
§26.10(v) Limiting Form
3: 26.1 Special Notation
x real variable.
4: 26.11 Integer Partitions: Compositions
§26.11 Integer Partitions: Compositions
A composition is an integer partition in which order is taken into account. … c ( n ) denotes the number of compositions of n , and c m ( n ) is the number of compositions into exactly m parts. c ( T , n ) is the number of compositions of n with no 1’s, where again T = { 2 , 3 , 4 , } . The integer 0 is considered to have one composition consisting of no parts: …