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Problem results

ProblemsClear skill: Set Partitions Permutations Build a practice set

COMB:9931153Let S(n,k) count partitions of [n] into k nonempty unordered blocks.

Set Partitions PermutationsStirling Second KindLast Element RecurrenceBoundary ValuesEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931154Mathematical problem title

Set Partitions PermutationsRestricted Growth StringsCanonical Block LabelsExplicit BijectionEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931155Mathematical problem title

Set Partitions PermutationsBlock Size ProfileEqual Size BlocksFactorial DivisionEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931156Mathematical problem title

Set Partitions PermutationsDistinguished RepresentativesPointed BlocksIdempotent FunctionsEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931157Mathematical problem title

Set Partitions PermutationsBell NumbersDistinguished BlockSubset RecurrenceEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931158Mathematical problem title

Set Partitions PermutationsFalling Factorial BasisFibre PartitionsPolynomial IdentityEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931159Mathematical problem title

Set Partitions PermutationsCycle NotationPermutation PowersInverse PermutationEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931160Let c(n,k) count permutations of [n] having exactly k disjoint cycles, including singleton cycles.

Set Partitions PermutationsStirling First KindCycle InsertionLast Label RecurrenceEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931161Mathematical problem title

Set Partitions PermutationsCycle Type CountingRotations Within CyclesRepeated Cycle LengthsEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931162Mathematical problem title

Set Partitions PermutationsCycle Count PolynomialRising FactorialSigned EvaluationEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931163Mathematical problem title

Set Partitions PermutationsMarked CycleDistinguished LabelTotal Cycle CountEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931164Mathematical problem title

Set Partitions PermutationsInvolutionsSingleton Pair DecompositionRecurrenceEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931165Mathematical problem title

Set Partitions PermutationsPermutation PowersAllowed Cycle LengthsFixed Point CountEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931166Mathematical problem title

Set Partitions PermutationsSigned Stirling InversionPolynomial BasesTriangular MatricesEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Mixed review

COMB:9931167Mathematical problem title

Set Partitions PermutationsInversion VectorLehmer CodePolynomial EnumeratorEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931168Prove that the smallest number of adjacent-entry swaps needed to sort a permutation into increasing order equals it…

Set Partitions PermutationsAdjacent SwapsInversion ParityCycle SignEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931169Mathematical problem title

Set Partitions PermutationsEulerian NumbersMaximum InsertionDescent RecurrenceEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931170Mathematical problem title

Set Partitions PermutationsOne DescentIncreasing RunsSubset EncodingEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931171A left-to-right maximum, or record, in a permutation word is an entry larger than every earlier entry; the first en…

Set Partitions PermutationsCycle Record BijectionLeft TO Right MaximaCanonical FormEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931172Mathematical problem title

Set Partitions PermutationsCyclic DescentsRotation OrbitsEulerian DistributionEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931309Mathematical problem title

Set Partitions PermutationsInvariant PartitionsLabel SymmetryEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931310Mathematical problem title

Set Partitions PermutationsPermutation RootsCycle InterleavingEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931312A partition of [n] is noncrossing if there do not exist a<b<c<d with a,c in one block and b,d in a different block.

Set Partitions PermutationsNoncrossing PartitionsBlock RefinementEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

COMB:9931313Mathematical problem title

Set Partitions PermutationsPartition LatticeMaximal ChainsEnumerative Combinatorics Problem Solving

Set partitions, Stirling numbers, and the cycle structure of permutationsEnumerative Combinatorics · Calculation

Showing 24 of 27 matching problems.