SemanticMathAdmin at 12:59, 12 August 2020

2020-08-12T12:59:33Z

← Older revision		Revision as of 12:59, 12 August 2020
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	*** arguments "{n}{k}"		*** arguments "{n}{k}"
	*** description "{the Stirling number of the first kind}"		*** description "{the Stirling number of the first kind}"
	Euleriannumber		** Euleriannumber
	*** parameters "{n}{k}"		*** parameters "{n}{k}"
	*** definitionurl "http://dlmf.nist.gov/26.14.SS1.p3"		*** definitionurl "http://dlmf.nist.gov/26.14.SS1.p3"

SemanticMathAdmin: Initial

2020-08-12T12:59:00Z

Initial

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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

Combinatorial Functions - Revision history

SemanticMathAdmin at 12:59, 12 August 2020

SemanticMathAdmin: Initial