Concepts5
∑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
∑MathIntermediate
Binomial Theorem and Identities
The binomial theorem expands (x + y)^n into a sum of terms using binomial coefficients that count how many ways to choose k items from n.
#binomial theorem#binomial coefficient#pascal's triangle+12
∑MathIntermediate
Stars and Bars
Stars and Bars counts the ways to distribute n identical items into k distinct bins using combinations.
#stars and bars#combinatorics#binomial coefficient+12