Concepts4
∑MathAdvanced
Pólya Enumeration
Pólya Enumeration Theorem generalizes Burnside’s Lemma by turning counting under symmetry into a polynomial substitution problem.
#pólya enumeration#cycle index#burnside lemma+12
∑MathAdvanced
Partition Function
The partition function p(n) counts the number of ways to write n as a sum of positive integers where order does not matter.
#partition function#integer partitions#euler pentagonal theorem+11
∑MathAdvanced
Stirling Numbers of First Kind
Stirling numbers of the first kind count permutations by their number of cycles and connect power polynomials to rising/falling factorials.
#stirling numbers of the first kind#unsigned cycle numbers#signed stirling numbers+12
⚙️AlgorithmAdvanced
Polynomial Operations
Fast polynomial operations treat coefficients like numbers but use FFT/NTT to multiply in O(n \log n) time instead of O(n^2).
#polynomial#ntt#fft+12