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  • Enumerative Combinatorics

Enumerative Combinatorics#

  • Introduction
  • Combinatorial Functions
    • Factorial(n): RngIntElt → RngIntElt
    • NumberOfPermutations(n, k): RngIntElt, RngIntElt → RngIntElt
    • Binomial(n, r): RngIntElt, RngIntElt → RngIntElt
    • Multinomial(n, [r₁, ... rₙ]): RngIntElt, [RngIntElt] → RngIntElt
    • Fibonacci(n): RngIntElt → RngIntElt
    • Catalan(n): RngIntElt → RngIntElt
    • Lucas(n): RngIntElt → RngIntElt
    • GeneralizedFibonacciNumber(g0, g1, n): RngIntElt, RngIntElt, RngIntElt → RngIntElt
    • StirlingFirst(n, k): RngIntElt, RngIntElt → RngIntElt
    • StirlingSecond(n, k): RngIntElt, RngIntElt → RngIntElt
    • Bell(n): RngIntElt → RngIntElt
    • EulerianNumber(n, r): RngIntElt, RngIntElt → RngIntElt
    • HarmonicNumber(n): RngIntElt → FldRatElt
    • BernoulliNumber(n): RngIntElt → FldRatElt
    • BernoulliApproximation(n): RngIntElt → FldPrElt
    • BernoulliPolynomial(n): RngIntElt → RngUPolElt
  • Subsets of a Finite Set
    • Subsets(S): SetEnum → SetEnum
    • Subsets(S, k): SetEnum, RngIntElt → SetEnum
    • Multisets(S, k): SetEnum, RngIntElt → SetEnum
    • Subsequences(S, k): SetEnum, RngIntElt → SetEnum
    • Permutations(S): SetEnum → SetEnum;
    • Permutations(S, k): SetEnum, RngIntElt → SetEnum;
    • Example: Odd Graph

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