Stirling numbers
Combinatorial partition enumerators
Stirling numbers are integers that arise in combinatorics when counting ways to partition or arrange objects.
Stirling numbers of the first kind count permutations by their number of cycles.
Stirling numbers of the second kind count ways to partition a set into a specified number of non-empty subsets: The Stirling number S(4,2) equals 7, representing seven ways to split four elements into two groups.
Return of something previous
- enumerationSequential listing of items
- factorialDescending multiplication of integers
- generating functionsPower series encoding sequences
- polynomialsExpressions with variable powers
identities · arrangements · subsets · asymptotic · labeled · unlabeled · counting · signed
Formula where terms depend on earlier ones
- generating functionsPower series encoding sequences
- transformationThorough change in form
Recurring sequences of events
- signedWrote one's name on
- unsignedBearing no signature
- permutationArrangement in specific order
- transpositionsRearrangements by switching positions
Obstructs or sections
- nonemptyHaving some contents
- disjointSeparate at connections
- refinementElegance of manner
- recurrenceReturn of something previous
recurrence
Return of something previous
- enumerationSequential listing of items
- factorialDescending multiplication of integers
- generating functionsPower series encoding sequences
polynomials · identities · arrangements · subsets · asymptotic · labeled · unlabeled · counting · signed · unsigned
recurrence relation
Formula where terms depend on earlier ones
- generating functionsPower series encoding sequences
- transformationThorough change in form
cycles
Recurring sequences of events
- signedWrote one's name on
- unsignedBearing no signature
- permutationArrangement in specific order
blocks
Obstructs or sections
- nonemptyHaving some contents
- disjointSeparate at connections
- refinementElegance of manner
- combinatoricspermutation, combinations, combination, counting, arrangements
- discrete mathcombinatorics, graph theory, set theory, number theory, proofs
- number sequencesFibonacci sequence, arithmetic sequence, integers, perfect squares, Pascal's triangle
- finite differences
- recursionrecursion, base case, self-reference, infinite recursion, recurrence relation