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Partition Theory
Undergraduate
Definition
Study of ways to represent positive integers as sums of positive integers
Formulas
p(n): partition number of n
Σp(n)xⁿ = ∏1/(1-xᵏ)
Euler identities
Hardy-Ramanujan asymptotic
Examples
Example 1
p(5) = 7: 5=4+1=3+2=3+1+1=...
Example 2
Young diagrams
Applications
Number theory
Representation theory
Physics
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