Combinatorial Functions

DLMF_CM

• defines
  • Stirlingnumbers
    • parameters null
    • equiv "combinat1:Stirling_s"
    • definitionurl "http://dlmf.nist.gov/26.8.SS1.p1"
    • signature "{\\Integers\\times\\Integers\\mapsto\\Integers}"
    • arguments "{n}{k}"
    • description "{the Stirling number of the first kind}"

Euleriannumber

• • • parameters "{n}{k}"
    • definitionurl "http://dlmf.nist.gov/26.14.SS1.p3"
    • signature "{\\Integers\\times\\Integers\\mapsto\\Integers}"
    • arguments null
    • description "{the Eulerian number}"
  • nrestcompositions
    • parameters null
    • definitionurl "http://dlmf.nist.gov/26.11#p1"
    • signature "{?\\mapsto\\Integers}"
    • arguments "{\\mathrm{condition}}{n}"
    • description "{the restricted number of compositions of $n$ into exactly $m$ parts}"
  • nplanepartitions
    • parameters null
    • definitionurl "http://dlmf.nist.gov/26.12.SS1.p4"
    • signature "{\\Integers\\mapsto\\Integers}"
    • arguments "{n}"
    • description "{the number of plane partitions of $n$}"
  • StirlingnumberS
    • parameters null
    • equiv "combinat1:Stirling_S"
    • definitionurl "http://dlmf.nist.gov/26.8.SS1.p3"
    • signature "{\\Integers\\times\\Integers\\mapsto\\Integers}"
    • arguments "{n}{k}"
    • description "{the Stirling number of the second kind}"
  • Catalannumber
    • parameters null
    • definitionurl "http://dlmf.nist.gov/26.5.E1"
    • signature "{\\Integers\\mapsto\\Integers}"
    • arguments "{n}"
    • description "{the Catalan number}"
  • nrestpartitions
    • parameters null
    • definitionurl "http://dlmf.nist.gov/26.10.SS1"
    • signature "{?\\mapsto\\Integers}"
    • arguments "{\\mathrm{condition}}{n}"
    • description "{the restricted number of partitions of $n$}"
  • binom
    • parameters "{z}{m}"
    • equiv "combinat1:binomial"
    • definitionurl "http://dlmf.nist.gov/1.2.SS1"
    • signature "{\\Complexes\\times\\Integers\\mapsto\\Complexes}"
    • arguments null
    • description "{the binomial coefficient}"
  • ncompositions
    • parameters null
    • definitionurl "http://dlmf.nist.gov/26.11#p1"
    • signature "{\\Integers\\mapsto\\Integers}"
    • arguments "{n}"
    • description "{the number of compositions of $n$}"
  • Bellnumber
    • parameters null
    • equiv "combinat1:Bell"
    • definitionurl "http://dlmf.nist.gov/26.7.SS1"
    • signature "{\\Integers\\mapsto\\Integers}"
    • arguments "{n}"
    • description "{the Bell number}"
  • npartitions
    • parameters null
    • definitionurl "http://dlmf.nist.gov/26.2#Px4.p2"
    • signature ""
    • arguments "{n}"
    • description "{the total number of partitions of $n$}"
  • Pochhammersym
    • parameters "{a}{n}"
    • equiv "hypergeo0:pochhammer"
    • definitionurl "http://dlmf.nist.gov/5.2.SS3"
    • signature "{\\Complexes\\times\\nonnegIntegers\\mapsto\\Complexes}"
    • arguments null
    • description "{the Pochhammer symbol (or shifted factorial)}"
  • LeviCivitasym
    • parameters "{i}{j}{k}"
    • definitionurl "http://dlmf.nist.gov/1.6.E14"
    • signature "{\\Integers\\times\\Integers\\times\\Integers\\mapsto\\{0,\\pm 1\\}}"
    • arguments null
    • description "{the Levi-Civita symbol}"
  • multinomial
    • parameters "{n}{n_1,n_2,\\ldots,n_k}"
    • equiv "combinat1:multinomial"
    • definitionurl "http://dlmf.nist.gov/26.4.SS1.p1"
    • signature "{\\Integers\\times\\Integers^k\\mapsto\\Integers}"
    • arguments null
    • description "{the multinomial coefficient}"
  • npermutations
    • parameters "{n}"
    • definitionurl "http://dlmf.nist.gov/26.13#p1"
    • signature "{\\Integers\\mapsto\\Integers}"
    • arguments null
    • description "{the number of permutations of $n$}"
  • date "2018-08-09"
  • version "0"
  • status "experimental"
  • description