How to resolve the algorithm Lah numbers step by step in the J programming language

Published on 12 May 2024 09:40 PM
#J

How to resolve the algorithm Lah numbers step by step in the J programming language

Table of Contents

Problem Statement

Lah numbers, sometimes referred to as Stirling numbers of the third kind, are coefficients of polynomial expansions expressing rising factorials in terms of falling factorials. Unsigned Lah numbers count the number of ways a set of n elements can be partitioned into k non-empty linearly ordered subsets. Lah numbers are closely related to Stirling numbers of the first & second kinds, and may be derived from them. Lah numbers obey the identities and relations:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Lah numbers step by step in the J programming language

Source code in the j programming language

NB. use:   k lah n
lah=: ! :(!&<: * %&!~)&x:  NB. `%~' is shorter than `*inv'

NB. wory_lah translates lah to algebraic English.
Monad =: :[:  NB. permit only a y argument 
Dyad =: [: :  NB. require x and y arguments
but_1st =: &
decrement =: <: Monad

NB. ! means either factorial or combinations (just as - means negate or subtract)
factorial =: ! Monad
combinations =: ! Dyad

into =: *inv Dyad
times =: *  Dyad
extend_precision =: x: Monad
wordy_lah =: ((combinations but_1st decrement) times (into but_1st factorial))but_1st extend_precision Dyad

You may also check:How to resolve the algorithm Idiomatically determine all the lowercase and uppercase letters step by step in the Common Lisp programming language
You may also check:How to resolve the algorithm Boolean values step by step in the Picat programming language
You may also check:How to resolve the algorithm Evaluate binomial coefficients step by step in the Fermat programming language
You may also check:How to resolve the algorithm Halt and catch fire step by step in the Hare programming language
You may also check:How to resolve the algorithm Pick random element step by step in the Déjà Vu programming language